Haiying Li

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An inequality between Jordan–von Neumann constant and James constant

2009-10-10

Changsen Yang , Haiying Li

A construction of the Hom-Yetter–Drinfeld category

2014-01-01

Haiying Li , Tianshui Ma

In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter–Drinfeld category $_H^H{\mathbb {YD}}$ via the Radford biproduct Hom-Hopf algebra, and prove … In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter–Drinfeld category $_H^H{\mathbb {YD}}$ via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter–Drinf

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Cobraided smash product Hom-Hopf algebras

2014-01-01

Tianshui Ma , Haiying Li , Tao Yang

Let $(A,\alpha )$ and $(B,\beta )$ be two Hom-Hopf algebras. We construct a new class of Hom-Hopf algebras: $R$-smash products $(A\mathbin {\natural _R} B,\alpha \otimes \beta )$. Moreover, necessary and … Let $(A,\alpha )$ and $(B,\beta )$ be two Hom-Hopf algebras. We construct a new class of Hom-Hopf algebras: $R$-smash products $(A\mathbin {\natural _R} B,\alpha \otimes \beta )$. Moreover, necessary and sufficient conditions for $(A\mathbin {\natural _R}

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On a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces

2015-04-15

Haiying Li , Zhitao Guo

The boundedness and compactness of a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces are investigated in this paper. The boundedness and compactness of a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces are investigated in this paper.

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On the braided structures of Radford's biproduct

2011-03-01

Tianshui Ma , Haiying Li , Zhao Wen-zheng

Composition operators between generally weighted Bloch spaces and $Q_{log}^q$ space

2009-01-01

Haiying Li , Пэйдэ Лю

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COMPOSITION OPERATORS BETWEEN GENERALLY WEIGHTED BLOCH SPACES OF POLYDISK

2007-01-01

Haiying Li , Пэйдэ Лю , Maofa Wang

Holomorphic self-map; Composition operator; Bloch space; Generally weighted Bloch space. Abstract: Let be a holomorphic self-map of the open unit polydisk U n in C n and p, q > … Holomorphic self-map; Composition operator; Bloch space; Generally weighted Bloch space. Abstract: Let be a holomorphic self-map of the open unit polydisk U n in C n and p, q > 0. In this paper, the generally weighted Bloch spaces B p (U n ) are introduced, and the boundedness and compactness of composition operator C from B p log (U n ) to B q log (U n ) are investigated.

General Hom–Lie algebra

2015-06-08

Tianshui Ma , Lihong Dong , Haiying Li

We introduce the notion of a general Hom–Lie algebra and show that any Hom-algebra in the category [Formula: see text], where [Formula: see text] is a triangular Hom–Hopf algebra, can … We introduce the notion of a general Hom–Lie algebra and show that any Hom-algebra in the category [Formula: see text], where [Formula: see text] is a triangular Hom–Hopf algebra, can give rise to a general Hom–Lie algebra, which generalizes the main result in [11] to the Hom-case.

Note on a Li-Stević integral-type operator from mixed-norm spaces to nth weighted spaces

2017-01-01

Haiying Li , Zhi ao Guo

The boundedness and compactness of a Li The boundedness and compactness of a Li

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On some product-type operators from area nevanlinna spaces to Zygmund-type spaces

2017-01-01

Haiying Li , Zhitao Guo

The boundedness and compactness of product-type operators and integral-type operators from area Nevanlinna spaces to Zygmund-type spaces and little Zygmund-type spaces are investigated The boundedness and compactness of product-type operators and integral-type operators from area Nevanlinna spaces to Zygmund-type spaces and little Zygmund-type spaces are investigated

On Radford Biproduct

2015-06-26

Tianshui Ma , Haiying Li

Let H be a bialgebra, A an algebra, and a left H-comodule coalgebra. Let f: H ⊗ H → A ⊗ H and R: H ⊗ A → A ⊗ … Let H be a bialgebra, A an algebra, and a left H-comodule coalgebra. Let f: H ⊗ H → A ⊗ H and R: H ⊗ A → A ⊗ H be two linear maps. Let B be a right H-module algebra and also a right H-comodule coalgebra. In this paper, necessary and sufficient conditions are given for the one-sided Brzeziński's crossed product algebra and the two-sided smash coproduct coalgebra A × H × B to form a bialgebra, which we call the Brzeziński's double biproduct. The celebrated Radford biproduct [18 Radford , D. E. ( 1985 ). The structure of Hopf algebra with a projection . J. Algebra 92 : 322 – 347 .[Crossref], [Web of Science ®] , [Google Scholar]], Majid's double biproduct [13 Majid , S. ( 1999 ). Double-bosonization of braided groups and the construction of U q (g) . Math. Proc. Cambridge Philos. Soc. 125 ( 1 ): 151 – 192 .[Crossref], [Web of Science ®] , [Google Scholar]], Agore and Militaru's unified product [2 Agore , A. L. , Militaru , G. ( 2011 ). Extending structures II: The quantum version . J. Algebra 336 : 321 – 341 .[Crossref], [Web of Science ®] , [Google Scholar]], and the Wang–Jiao–Zhao's crossed product [21 Wang , S. H. , Jiao , Z. M. , Zhao , W. Z. ( 1998 ). Hopf algebra structures on crossed products . Comm. Algebra 26 : 1293 – 1303 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]] are all derived as special cases. On the other hand, we construct a class of Radford biproducts by a twisting method.

WEIGHTED COMPOSITION OPERATORS BETWEEN H∞ AND GENERALLY WEIGHTED BLOCH SPACES ON POLYDISKS

2010-01-01

Haiying Li , Пэйдэ Лю

Let Un be the unit polydisk of Cn, φ(z) = (φ1(z),φ2(z),…,φn(z)) be a holomorphic self-map of Un and ψ be a holomorphic function on Un. H∞(Un) is the space of … Let Un be the unit polydisk of Cn, φ(z) = (φ1(z),φ2(z),…,φn(z)) be a holomorphic self-map of Un and ψ be a holomorphic function on Un. H∞(Un) is the space of all bounded holomorphic functions on Un and by a generally weighted Bloch space we mean . We give necessary and sufficient conditions of the boundedness and compactness of the weighted composition operator ψCφ between H∞(Un) and .

A construction of Hom-Yetter-Drinfeld category

2016-01-01

Haiying Li , Tianshui Ma

In continuation of our recent work about smash product Hom-Hopf algebras in \cite{MLY}, we introduce Hom-Yetter-Drinfeld category $_H^H{\mathbb{YD}}$ via Radford biproduct Hom-Hopf algebra, and prove that the Hom-Yetter-Drinfeld modules can … In continuation of our recent work about smash product Hom-Hopf algebras in \cite{MLY}, we introduce Hom-Yetter-Drinfeld category $_H^H{\mathbb{YD}}$ via Radford biproduct Hom-Hopf algebra, and prove that the Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and $_H^H{\mathbb{YD}}$ is a pre-braided tensor category, where $(H, \b, S)$ is a Hom-Hopf algebra. Furthermore, we obtain that $(A^{\natural}_{\diamond} H,\a\o \b)$ is a Radford biproduct Hom-Hopf algebra if and only if $(A,\a)$ is a Hopf algebra in the category $_H^H{\mathbb{YD}}$. At last, some examples and applications are given.

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Powers of an Invertible (s, p)—w—Hyponormal Operator

2008-04-01

Haiying Li

Double biproduct Hom-bialgebra and related quasitriangular structures

2016-10-21

Tianshui Ma , Haiying Li , Linlin Liu

Generalized von Neumann–Jordan constant for the Banaś–Frączek space

2018-01-01

Changsen Yang , Haiying Li

The exact value of the generalized von Neumann–Jordan constant is found for the Banaś–Frączek space $\mathbb {R}^2_\lambda $: $C^{(p)}_{\rm NJ}(\mathbb {R}^2_\lambda )=1+(1-{1/\lambda ^{2}})^{{p/2}}$ ($\lambda \gt 1$, $p\geq 2$, $\lambda ^2(1-{1/\lambda … The exact value of the generalized von Neumann–Jordan constant is found for the Banaś–Frączek space $\mathbb {R}^2_\lambda $: $C^{(p)}_{\rm NJ}(\mathbb {R}^2_\lambda )=1+(1-{1/\lambda ^{2}})^{{p/2}}$ ($\lambda \gt 1$, $p\geq 2$, $\lambda ^2(1-{1/\lambda ^

Convergence analysis for solving equilibrium problems and split feasibility problems in Hilbert spaces

2022-03-17

Haiying Li , Yulian Wu , Fenghui Wang

In this article, we propose four alternated inertial algorithms for finding a common solution of equilibrium problems and split feasibility problems in Hilbert spaces. We present a variable step size, … In this article, we propose four alternated inertial algorithms for finding a common solution of equilibrium problems and split feasibility problems in Hilbert spaces. We present a variable step size, which is not required to know the operator norm. Furthermore, these algorithms adopt the new convex subset form by a sequence of closed balls instead of half spaces, and it is easy to calculate the projections onto these sets. We establish strong and weak convergence theorems of these algorithms under some proper assumptions and also present a numerical experiment to illustrate the performance and the advantage of the proposed algorithms.

A class of new braided Hopf algebras

2010-12-31

Tianshui Ma , Haiying Li , Shuanhong Wang

QUASITRIANGULARITY OF BRZEZIŃSKI'S CROSSED COPRODUCTS

2011-03-30

Tianshui Ma , Haiying Li , Shuanhong Wang

In continuation of our recent work about the quasitriangular structures for the twisted tensor biproduct, we give the necessary and sufficient conditions for Brzeziński crossed coproduct coalgebra, including the twisted … In continuation of our recent work about the quasitriangular structures for the twisted tensor biproduct, we give the necessary and sufficient conditions for Brzeziński crossed coproduct coalgebra, including the twisted tensor coproduct introduced by Caenepeel, Ion, Militaru and Zhu and crossed coproduct as constructed by Lin, equipped with the usual tensor product algebra structure to be a Hopf algebra. Furthermore, the necessary and sufficient conditions for Brzeziński crossed coproduct to be a quasitriangular Hopf algebra are obtained.

Products of integral-type and composition operators from generally weighted Bloch space to F(p,q,s) space

2009-01-01

Haiying Li , Yang Xiang-zhao

Products of integral-type and composition operators has been recently introduced by Li and Stevic and studied in a series of their papers. In this note we study the boundedness and … Products of integral-type and composition operators has been recently introduced by Li and Stevic and studied in a series of their papers. In this note we study the boundedness and compactness of these products from generally weighted Bloch space to F(p; q; s) space, where 0 < p; s < ?; q > -2; ? > 0.

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An inequality on Jordan-von Neumann constant and James constant on Z_p,q space

2013-01-01

Changsen Yang , Haiying Li

Let λ > 0 , Z p,q denote R 2 endowed with the normRecently, James constant J(Z p,q ) and von Neumann-Jordan constant C NJ (Z p,q ) have been … Let λ > 0 , Z p,q denote R 2 endowed with the normRecently, James constant J(Z p,q ) and von Neumann-Jordan constant C NJ (Z p,q ) have been investigated under the two cases of a space 2 p q ∞ and 1 p q 2 .In this note, we show an inequality on these two constants under the case of 1 p 2 q ∞ .As an application, we give a sufficient condition for the space Z p,q with uniform normal structure.

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Convexities of Gaussian integral means and weighted integral means for analytic functions

2018-08-24

Haiying Li , Can Liu

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Some properties of (m,C)-isometric operators

2019-01-01

Haiying Li , Yaru Wang

In this paper, we study if T is an (m,C)-isometric operator and CT+C commutes with T, then T+ is an (m,C)-isometric operator. We also give local spectral properties and spectral … In this paper, we study if T is an (m,C)-isometric operator and CT+C commutes with T, then T+ is an (m,C)-isometric operator. We also give local spectral properties and spectral relations of (m;C)-isometric operators, such as property (?), decomposability, the single-valued extension property and Dunford?s boundedness. We also investigate perturbation of (m,C)-isometric operators by nilpotent operators and by algebraic operators and give some properties.

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Strong convergence of iterative sequences for nonexpansive mappings

2009-05-05

Yisheng Song , Haiying Li

Weighted composition operators between generally weighted Bloch spaces of polydisk

2010-01-25

Haiying Li , Пэйдэ Лю

A class of braided monoidal categories via quasitriangular Hopf π-crossed coproduct algebras

2014-05-22

Tianshui Ma , Linlin Liu , Haiying Li

Let π be a group and (H = {H α } α∈π , μ, η) a Hopf π-algebra. First, we introduce the concept of quasitriangular Hopf π-algebra, and then prove … Let π be a group and (H = {H α } α∈π , μ, η) a Hopf π-algebra. First, we introduce the concept of quasitriangular Hopf π-algebra, and then prove that the left H-π-module category [Formula: see text], where (H, R) is a quasitriangular Hopf π-algebra, is a braided monoidal category. Second, we give the construction of Hopf π-crossed coproduct algebra [Formula: see text]. At last, the necessary and sufficient conditions for [Formula: see text] to be a quasitriangular Hopf π-algebra are derived, and in this case, [Formula: see text] is a braided monoidal category.

On the James type constant of l p − l 1

2015-03-03

Changsen Yang , Haiying Li

For any $\tau\geq0$ , $t\geq1$ and $p\geq1$ , the exact value of the James type constant $J_{X,t}(\tau)$ of the $l_{p}-l_{1}$ space is investigated. As an application, the exact value of … For any $\tau\geq0$ , $t\geq1$ and $p\geq1$ , the exact value of the James type constant $J_{X,t}(\tau)$ of the $l_{p}-l_{1}$ space is investigated. As an application, the exact value of the von Neuman-Jordan type constant of the $l_{p}-l_{1}$ space can also be obtained.

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Characterizations of Closed Ideals and Main Parts of Some Analytic and Meromorphic Classes of Area Nevanlinna Type

2011-01-01

Romi F. Shamoyan , Haiying Li

We provide a complete description of closed ideals of some analytic area Nevanlinna-type classes in the unit disk and characterize main parts of Loran expansions of certain meromorphic spaces in … We provide a complete description of closed ideals of some analytic area Nevanlinna-type classes in the unit disk and characterize main parts of Loran expansions of certain meromorphic spaces in the unit disk defined with the help of Nevanlinna characteristic.

Convergence of Taylor series in Fock spaces

2014-01-01

Haiying Li

It is well known that the Taylor series of every function in the Fock space $F^p_\alpha $ converges in norm when $1< p< \infty $. It is also known that … It is well known that the Taylor series of every function in the Fock space $F^p_\alpha $ converges in norm when $1< p< \infty $. It is also known that this is no longer true when $p=1$. In this note we consider the case $0< p< 1$ and show that the Tayl

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Properties of p-ω-hyponormal operators

2006-03-01

Changsen Yang , Haiying Li

The James constant for the l 3 − l 1 space

2016-08-15

Chang Sen Yang , Haiying Li

Construction of a braided monoidal category for Brzeziński crossed coproducts of Hopf $\pi $-algebras

2017-01-01

Tianshui Ma , Haiying Li , Shaoxian Xu

Let $\pi $ be a group, $C, H$ Hopf $\pi $-algebras, and $g_{\alpha }: C_{\alpha }\otimes H_{\alpha }\rightarrow H_{\alpha }\otimes H_{\alpha }$ and $T_{\alpha }: C_{\alpha }\otimes H_{\alpha }\rightarrow H_{\alpha … Let $\pi $ be a group, $C, H$ Hopf $\pi $-algebras, and $g_{\alpha }: C_{\alpha }\otimes H_{\alpha }\rightarrow H_{\alpha }\otimes H_{\alpha }$ and $T_{\alpha }: C_{\alpha }\otimes H_{\alpha }\rightarrow H_{\alpha }\otimes C_{\alpha }$ families of linear

Volterra composition operators from generally weighted Bloch spaces to Bloch-type spaces on the unit ball

2012-12-12

Haiying Li , Haixia Zhang

Let ϕ be a holomorphic self-map of the open unit ball B, g ∈ H(B).In this paper, the boundedness and compactness of the Volterra composition operator T ϕ g from … Let ϕ be a holomorphic self-map of the open unit ball B, g ∈ H(B).In this paper, the boundedness and compactness of the Volterra composition operator T ϕ g from generally weighted Bloch spaces to Bloch-type spaces are investigated.

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Two Results on Brzeziński π-crossed Product

2014-01-16

Tianshui Ma , Haiying Li , Zhicheng Zhang

We give the necessary and sufficient conditions for a family of Brzezínski crossed product algebras with suitable comultiplication and counit to be a Hopf π-coalgebra. On the other hand, necessary … We give the necessary and sufficient conditions for a family of Brzezínski crossed product algebras with suitable comultiplication and counit to be a Hopf π-coalgebra. On the other hand, necessary and sufficient conditions for the Brzeziński π-crossed product A⧫H to be a coquasitriangular Hopf π-coalgebra are derived, then the category A⧫H ℳ of the left π-comodules over A⧫H is braided.

On m-skew complex symmetric operator

2018-04-06

Haiying Li , Wang Yaru

In this paper, the definition of m-skew complex symmetric operators is introduced.Firstly, we prove that ∆ - m (T ) is complex symmetric with the conjugation C and give some … In this paper, the definition of m-skew complex symmetric operators is introduced.Firstly, we prove that ∆ - m (T ) is complex symmetric with the conjugation C and give some properties of ∆ - m (T ).Secondly, let T be m-skew complex symmetric with conjugation C, if n is odd, then T n is m-skew complex symmetric with conjugation C; if n is even, with the assumption T * CT C = CT CT * , then T n is m-complex symmetric with conjugation C. Finally, we give some properties of m-skew complex symmetric operators.

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WEIGHTED COMPOSITION OPERATORS BETWEEN H<sup>∞</sup> AND GENERALLY WEIGHTED BLOCH SPACES ON POLYDISKS

2010-03-23

Haiying Li , Пэйдэ Лю

Let U n be the unit polydisk of C n , φ(z) = (φ 1 (z),φ 2 (z),…,φ n (z)) be a holomorphic self-map of U n and ψ be … Let U n be the unit polydisk of C n , φ(z) = (φ 1 (z),φ 2 (z),…,φ n (z)) be a holomorphic self-map of U n and ψ be a holomorphic function on U n . H ∞ (U n ) is the space of all bounded holomorphic functions on U n and by a generally weighted Bloch space we mean [Formula: see text]. We give necessary and sufficient conditions of the boundedness and compactness of the weighted composition operator ψC φ between H ∞ (U n ) and [Formula: see text].

Erratum to: On the James type constant of l p − l 1

2015-04-23

Changsen Yang , Haiying Li

The online version of the original article can be found under doi: 10.1186/s13660-015-0598-3 . The online version of the original article can be found under doi: 10.1186/s13660-015-0598-3 .

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Generalized Composition Operators from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℬ</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Spaces to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><…

2014-01-01

Haiying Li , Tianshui Ma

Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>p</mml:mi><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:math>, let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mo><</mml:mo><mml:mi>q</mml:mi><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:math>, and let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>φ</mml:mi></mml:mrow></mml:math>be an analytic self-map of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>𝔻</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mi>g</mml:mi><mml:mo>∈</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>𝔻</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>. The boundedness and compactness of generalized composition operators<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mo … Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mn>0</mml:mn><mml:mo><</mml:mo><mml:mi>p</mml:mi><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:math>, let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:mo>-</mml:mo><mml:mn>2</mml:mn><mml:mo><</mml:mo><mml:mi>q</mml:mi><mml:mo><</mml:mo><mml:mi>∞</mml:mi></mml:math>, and let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:mrow><mml:mi>φ</mml:mi></mml:mrow></mml:math>be an analytic self-map of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:mrow><mml:mi>𝔻</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><mml:mi>g</mml:mi><mml:mo>∈</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>𝔻</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>. The boundedness and compactness of generalized composition operators<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>φ</mml:mi></mml:mrow><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:msubsup><mml:mi>f</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy="false">∫</mml:mo><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mi>z</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi mathvariant="normal">‍</mml:mi></mml:mrow></mml:mrow><mml:msup><mml:mrow><mml:mi>f</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">'</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:mi>φ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ξ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo><mml:mi>g</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>ξ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>d</mml:mi><mml:mi>ξ</mml:mi><mml:mo>, </mml:mo><mml:mi>z</mml:mi><mml:mo>∈</mml:mo><mml:mi>𝔻</mml:mi><mml:mo>, </mml:mo><mml:mi>f</mml:mi><mml:mo>∈</mml:mo><mml:mi>H</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>𝔻</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>, from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M9"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℬ</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M10"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℬ</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>) spaces to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M11"><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>spaces are investigated.

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A NOTE ON NEW ESTIMATES FOR DISTANCES IN ANALYTIC FUNCTION SPACES

2010-02-13

Romi F. Shamoyan , Haiying Li

We provide new estimates for distances from fixed analytic functions to their subspaces in the unit disk.We will enlarge the list of previously known assertions of this type obtained recently … We provide new estimates for distances from fixed analytic functions to their subspaces in the unit disk.We will enlarge the list of previously known assertions of this type obtained recently by R. Zhao and W. Xu.

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Matrix-geometric solution of a heterogeneous two-Server M/(PH,M)/2 queueing system with server breakdowns

2010-05-01

Dequan Yue , Ling Wang , Tingting Xu +1 more

In this paper, we study a repairable queueing system with two different servers, where Server 1 is perfectly reliable and Server 2 is subject to breakdown. The service times of … In this paper, we study a repairable queueing system with two different servers, where Server 1 is perfectly reliable and Server 2 is subject to breakdown. The service times of two servers are assumed to follow phase type (PH) distribution and exponential distribution, respectively. By establishing the quasi-birth-and-death (QBD) process of the system states, we first derive the equilibrium condition of the system, and then obtain the matrix-geometric solution for the steady-state probability vectors of the system. Finally, numerical results are presented.

Products of composition and n-th differentiation operators from α-bloch space to Qp space

2013-01-01

Haiying Li , Cui Wang , Tianyu Xue +1 more

Let ? be an analytic self-map of the open unit disk D on the complex plane and ? > 0, p ? 0, n ? N. In this paper, the … Let ? be an analytic self-map of the open unit disk D on the complex plane and ? > 0, p ? 0, n ? N. In this paper, the boundedness and compactness of the products of composition operators and nth differentiation operators C?Dn from a-Bloch space B? and B?0 to Qp space are investigated.

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On characterizations of main parts of some meromorphic classes of area Nevanlinna type in the unit disk

2011-01-01

Romi F. Shamoyan , Haiying Li

−1,β ≥ 0,0 < p < ∞.Let further B(z) be a classical Blaschke product (see [2]). For ourexposition we will need two types of special sequences in the unit disk … −1,β ≥ 0,0 < p < ∞.Let further B(z) be a classical Blaschke product (see [2]). For ourexposition we will need two types of special sequences in the unit disk Dsampling sequences and Carleson sequences.The sampling sequence in D is a sequence in unit disk D such thatfor τ ∈ (0,1],D =S

Cobraided Smash Product Hom-Hopf Algebras

2016-01-01

Tianshui Ma , Haiying Li , Tao Yang

Let $(A,\a)$ and $(B,\b)$ be two Hom-Hopf algebras. In this paper, we construct a class of new Hom-Hopf algebras: $R$-smash product $(A\natural_R B,\a\o \b)$. Moreover, necessary and sufficient conditions for … Let $(A,\a)$ and $(B,\b)$ be two Hom-Hopf algebras. In this paper, we construct a class of new Hom-Hopf algebras: $R$-smash product $(A\natural_R B,\a\o \b)$. Moreover, necessary and sufficient conditions for $(A\natural_R B,\a\o \b)$ to be a cobraided Hom-Hopf algebra are given.

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On the Coquasitriangular Structures of Crossed Products

2012-01-01

Haiying Li

Let H be a Hopf algebra and weak action on the algebra A,σ∶HH→A a linear map.Then the Hopf crossed product A#σ H is obtained.It is obvious that A#σ H is … Let H be a Hopf algebra and weak action on the algebra A,σ∶HH→A a linear map.Then the Hopf crossed product A#σ H is obtained.It is obvious that A#σ H is not the smash-type product A#R H.Recently the coquasitriangular structures on some smash-type products have been studied.This paper gives the necessary and sufficient conditions for crossed product to be a coquasitriangular Hopf algebra.

On p-ω-hyponormal Operators

2005-01-01

Haiying Li

In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair … In this paper, we show that if T is p-ω-hyponormal, the nonzero points of the approximate and joint approximate point spectrum of T are identical; Moreover, we obtain a pair of inequalities similar to p-ω-hyponormal operators.

Thinking of the retail job of the newspaper and periodicals

2010-01-01

Haiying Li

Incidental to the development of the market economy, competition between the newspapers no longer limited to the competition, but will rise to the marketing that newspaper publishers such a product … Incidental to the development of the market economy, competition between the newspapers no longer limited to the competition, but will rise to the marketing that newspaper publishers such a product dimension. the value as a kind of information dissemination tool, the spread of the objects are tens of thousands of readers, will the readers to the newspapers concerned about the economic attention eyeball economy or to advertisers. And faced with technological development and distribution over the newspaper today facing not only from the various newspaper and periodicals of competition between from the media, television network for the competition among various media. in the press is facing deepen cultural restructuring in the background of the new market circumstances to do the work to improve the issue of management, a better play to the issue in press economy.

Best Possibility of the Furuta-type Inequality's Power with Negative Powers

2003-01-01

Haiying Li

In this paper, we prove that the power of the Furuta-type inequality with negative powers is best possible. We use the way which is different from Furuta's. In this paper, we prove that the power of the Furuta-type inequality with negative powers is best possible. We use the way which is different from Furuta's.

On an Integral-type Operator from the Generally Weighted Bloch Space to the Bloch-type Space

2011-01-01

Haiying Li

Let g∈H(B),g(0)=0 and φ is a holomorphic self-map of B.The boundedness and compactness of the operator Pgφ from the generally weighted Bloch space to the Bloch-type space on the unit … Let g∈H(B),g(0)=0 and φ is a holomorphic self-map of B.The boundedness and compactness of the operator Pgφ from the generally weighted Bloch space to the Bloch-type space on the unit ball are investigated.

On p-ω-hyponormal operators

2004-01-01

Haiying Li

Some Results about Vector Measure and an Counter Example about a Martingale

2003-01-01

Haiying Li

This article chiefly introduces some results about vector measure and gives an asymptotic martingale which is L1(u,X) bounded amart,not(B)-bounded. This article chiefly introduces some results about vector measure and gives an asymptotic martingale which is L1(u,X) bounded amart,not(B)-bounded.

Clinical value of CA125, AFP, and CEA for combined diagnosis and assessment of gastric cancer prognosis

2025-05-08

Yuchen Jia , Yajuan Wang , Haiying Li +2 more

To analyze the diagnostic and prognostic value of combined detection of CA125, AFP, and CEA for gastric cancer. Ninety-eight gastric cancer patients treated in our hospital from January 2020 to … To analyze the diagnostic and prognostic value of combined detection of CA125, AFP, and CEA for gastric cancer. Ninety-eight gastric cancer patients treated in our hospital from January 2020 to November 2022 were retrospectively selected and classified into the gastric cancer group according to screening criteria, while 80 patients diagnosed with benign gastric lesions during the same period were classified into the benign group. Serum levels of CA125, AFP, CEA, and their positive rates were significantly higher in the gastric cancer group compared to the benign group (P<0.05). The AUCs for CA125, AFP, CEA, and their combined detection in diagnosing gastric cancer were 0.815, 0.813, 0.911, and 0.919, respectively (P<0.001). In patients with stage III-IV, the levels of CA125, AFP, and CEA were higher than those in stage I-II (P<0.05). The AUCs for serum CA125, AFP, CEA, and their combined detection in TNM staging of gastric cancer were 0.751, 0.834, 0.911, and 0.931, respectively (P<0.001). Poorly differentiated patients had higher levels of CA125, AFP, and CEA compared to moderately to well-differentiated patients (P<0.05). The AUCs for serum CA125, AFP, CEA, and their combined detection in diagnosing differentiation degree were 0.819, 0.883, 0.746, and 0.986, respectively (P<0.001). Patients with metastasis had higher levels of CA125, AFP, and CEA compared to those without metastasis (P<0.05). The AUCs for serum CA125, AFP, CEA, and their combined detection in diagnosing metastasis were 0.716, 0.825, 0.863, and 0.892, respectively (P<0.001). The levels of CA125, AFP, and CEA of patients in the death group were higher than those in the survival group (P<0.05). The AUCs for serum CA125, AFP, CEA, and their combined detection in predicting clinical outcomes of gastric cancer patients were 0.713, 0.809, 0.922, and 0.926, respectively (P<0.001). Cox regression analysis indicated that TNM staging, peritoneal metastasis, and elevated CEA levels were independent risk factors for poor prognosis (mortality) in patients with gastric cancer (P<0.05). Serum levels of CA125, AFP, and CEA in patients with gastric cancer were significantly elevated and were correlated with the degree of differentiation and TNM staging. Combined detection had diagnostic efficacy in assessing metastasis and clinical outcomes.

Two novel golden ratio algorithms for quasimonotone variational inequalities

2025-04-18

Haiying Li , Wang Xing-fang

In this article, we provide two viscosity-type golden ratio algorithms with different inertial terms for solving quasimonotone variational inequalities in real Hilbert spaces. Both of our algorithms use a new … In this article, we provide two viscosity-type golden ratio algorithms with different inertial terms for solving quasimonotone variational inequalities in real Hilbert spaces. Both of our algorithms use a new adaptive step size which is based on the golden ratio $(\sqrt{5}+1)/2$. Under some suitable conditions, we obtain strong convergence theorems of our proposed algorithms. Moreover, several numerical results are given to illustrate the efficiency and advantages of our proposed methods.

On the constant $C^{(p)}_{NJ}(X)$ for the generalized Bana\'{s}-Fr\c{a}czek space

2025-04-11

Haiying Li , Xiangrun Yang , Changsen Yang

In this paper, we will study the generalized von Neumann-Jordan constant $C^{(p)}_{NJ}(X)$ for the generalized Bana\'{s}-Fr\c{a}czek space and improve related results on the Bana\'{s}-Fr\c{a}czek space. The exact value of $C^{(p)}_{NJ}(X)$ … In this paper, we will study the generalized von Neumann-Jordan constant $C^{(p)}_{NJ}(X)$ for the generalized Bana\'{s}-Fr\c{a}czek space and improve related results on the Bana\'{s}-Fr\c{a}czek space. The exact value of $C^{(p)}_{NJ}(X)$ will be calculated for $X$ to be the generalized Bana\'{s}-Fr\c{a}czek space $\mathbb{R}^2_{a,b,p_1}$ in the case $p\geq2$ such that $p_1\geq p\geq2$ or $p\geq p_1 \geq1$.

On (n, p)-th von Neumann-Jordan constants for Banach spaces

2024-01-01

Haiying Li , Xiang un Yang , Changsen Yang

In this paper, we introduce and discuss the upper, lower, upper modified and lower modified (n, p) -th von Neumann-Jordan constant for p 1 , which is a further generalization … In this paper, we introduce and discuss the upper, lower, upper modified and lower modified (n, p) -th von Neumann-Jordan constant for p 1 , which is a further generalization for von Neumann-Jordan constant in Banach spaces.We give some relationships between these constants and characterize uniformly nonl 1 n Banach spaces by upper and upper modified (n, p)th von Neumann-Jordan constant.Moreover, the exact value of this constant is calculated for the spaces l p , L p and l l 1 .

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On the Lyj(λ,μ,x) constant for the regular octagon space

2024-01-01

Xuemei Yang , Haiying Li , Changsen Yang

In this paper, we will investigate a class of geometric constants for a non-Hilbert space X satisfying James constant J(X)=?2. Specifically, the exact values of Lyj(?,?,X) and L?yj(?,?,X) will be … In this paper, we will investigate a class of geometric constants for a non-Hilbert space X satisfying James constant J(X)=?2. Specifically, the exact values of Lyj(?,?,X) and L?yj(?,?,X) will be calculated for the regular octagon space X, which improve the estimation obtained by Q. Liu et al.

When Leibniz Bialgebras are Nijenhuis?

2023-01-01

Haiying Li , Tianshui Ma , Shuanhong Wang

Leibniz algebras can be seen as a "non-commutative" analogue of Lie algebras. Nijenhuis operators on Leibniz algebras introduced by Cari\~{n}ena, Grabowski, and Marmo in [J. Phys. A: Math. Gen. 37(2004)] … Leibniz algebras can be seen as a "non-commutative" analogue of Lie algebras. Nijenhuis operators on Leibniz algebras introduced by Cari\~{n}ena, Grabowski, and Marmo in [J. Phys. A: Math. Gen. 37(2004)] are (1, 1)-tensors with vanishing Nijenhuis torsion. Recently triangular Leibniz bialgebras were introduced by Tang and Sheng in [J. Noncommut. Geom. 16(2022)] via the twisting theory of twilled Leibniz algebras. In this paper we find that Leibniz algebras are very closely related to Nijenhuis operators, and prove that a triangular symplectic Leibniz bialgebra together with a dual triangular structure must possess Nijenhuis operators, which makes it possible to study Nijehhuis geometry from the perspective of Leibniz algebras. At the same time, we regain the classical Leibniz Yang-Baxter equation by using the tensor form of classical $r$-matrics. At last we give the classification of triangular Leibniz bialgebras of low dimensions.

The directional testes asymmetry increases with temperature in seven plateau brown frog (Rana kukunoris) populations

2022-04-29

Haiying Li , Man Jun Shang , Jie Guo +3 more

Environmental stress is generally regarded as an important evolutionary force for promoting the differentiation of shape, structure and function of animal organs closely related to survival and reproduction. Geographical variation … Environmental stress is generally regarded as an important evolutionary force for promoting the differentiation of shape, structure and function of animal organs closely related to survival and reproduction. Geographical variation of temperature and corresponding change in intensity of male-male competition might drive inter-population differences in directional testes asymmetry (DTA). Here, we investigated inter-population variation in DTA of the brown frog (Rana kukunoris) at seven different altitudes on the eastern Tibetan Plateau. We found that the size of right testes increased with temperature, but not left testes. We also found that male age, body mass or body condition, and testis mass had not effect on DTA, suggesting that heavier or older R. kukunoris males or those with larger testes had not stronger DTA. The operational sex ratio did not affect DTA, but there was a positive correlation between DTA and temperature, suggesting that differences in the length of activity period and resources availability across locations may affect the energy budget of this frog, resulting in a gradual change in reproduction energy parallel to increasing temperature.

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Convergence analysis for solving equilibrium problems and split feasibility problems in Hilbert spaces

2022-03-17

Haiying Li , Yulian Wu , Fenghui Wang

Some properties of (m,C)-isometric operators

2019-01-01

Haiying Li , Yaru Wang

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Convexities of Gaussian integral means and weighted integral means for analytic functions

2018-08-24

Haiying Li , Can Liu

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On m-skew complex symmetric operator

2018-04-06

Haiying Li , Wang Yaru

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Generalized von Neumann–Jordan constant for the Banaś–Frączek space

2018-01-01

Changsen Yang , Haiying Li

Note on a Li-Stević integral-type operator from mixed-norm spaces to nth weighted spaces

2017-01-01

Haiying Li , Zhi ao Guo

The boundedness and compactness of a Li The boundedness and compactness of a Li

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Construction of a braided monoidal category for Brzeziński crossed coproducts of Hopf $\pi $-algebras

2017-01-01

Tianshui Ma , Haiying Li , Shaoxian Xu

On some product-type operators from area nevanlinna spaces to Zygmund-type spaces

2017-01-01

Haiying Li , Zhitao Guo

Double biproduct Hom-bialgebra and related quasitriangular structures

2016-10-21

Tianshui Ma , Haiying Li , Linlin Liu

The James constant for the l 3 − l 1 space

2016-08-15

Chang Sen Yang , Haiying Li

A construction of Hom-Yetter-Drinfeld category

2016-01-01

Haiying Li , Tianshui Ma

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Cobraided Smash Product Hom-Hopf Algebras

2016-01-01

Tianshui Ma , Haiying Li , Tao Yang

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The James Constant for the l3 -l1 Space

2016-01-01

Changsen Yang , Haiying Li

On Radford Biproduct

2015-06-26

Tianshui Ma , Haiying Li

General Hom–Lie algebra

2015-06-08

Tianshui Ma , Lihong Dong , Haiying Li

Erratum to: On the James type constant of l p − l 1

2015-04-23

Changsen Yang , Haiying Li

The online version of the original article can be found under doi: 10.1186/s13660-015-0598-3 . The online version of the original article can be found under doi: 10.1186/s13660-015-0598-3 .

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On a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces

2015-04-15

Haiying Li , Zhitao Guo

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On the James type constant of l p − l 1

2015-03-03

Changsen Yang , Haiying Li

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A class of braided monoidal categories via quasitriangular Hopf π-crossed coproduct algebras

2014-05-22

Tianshui Ma , Linlin Liu , Haiying Li

Two Results on Brzeziński π-crossed Product

2014-01-16

Tianshui Ma , Haiying Li , Zhicheng Zhang

Generalized Composition Operators from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi>ℬ</mml:mi></mml:mrow><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>Spaces to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>p</mml:mi><…

2014-01-01

Haiying Li , Tianshui Ma

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Convergence of Taylor series in Fock spaces

2014-01-01

Haiying Li

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Cobraided smash product Hom-Hopf algebras

2014-01-01

Tianshui Ma , Haiying Li , Tao Yang

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A construction of the Hom-Yetter–Drinfeld category

2014-01-01

Haiying Li , Tianshui Ma

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Products of composition and n-th differentiation operators from α-bloch space to Qp space

2013-01-01

Haiying Li , Cui Wang , Tianyu Xue +1 more

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An inequality on Jordan-von Neumann constant and James constant on Z_p,q space

2013-01-01

Changsen Yang , Haiying Li

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Volterra composition operators from generally weighted Bloch spaces to Bloch-type spaces on the unit ball

2012-12-12

Haiying Li , Haixia Zhang

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On the Coquasitriangular Structures of Crossed Products

2012-01-01

Haiying Li

QUASITRIANGULARITY OF BRZEZIŃSKI'S CROSSED COPRODUCTS

2011-03-30

Tianshui Ma , Haiying Li , Shuanhong Wang

On the braided structures of Radford's biproduct

2011-03-01

Tianshui Ma , Haiying Li , Zhao Wen-zheng

Characterizations of Closed Ideals and Main Parts of Some Analytic and Meromorphic Classes of Area Nevanlinna Type

2011-01-01

Romi F. Shamoyan , Haiying Li

On characterizations of main parts of some meromorphic classes of area Nevanlinna type in the unit disk

2011-01-01

Romi F. Shamoyan , Haiying Li

On an Integral-type Operator from the Generally Weighted Bloch Space to the Bloch-type Space

2011-01-01

Haiying Li

Products of integral-type and composition operators between generally weighted Bloch spaces.

2011-01-01

Haiying Li , Tianshui Ma

A class of new braided Hopf algebras

2010-12-31

Tianshui Ma , Haiying Li , Shuanhong Wang

Matrix-geometric solution of a heterogeneous two-Server M/(PH,M)/2 queueing system with server breakdowns

2010-05-01

Dequan Yue , Ling Wang , Tingting Xu +1 more

WEIGHTED COMPOSITION OPERATORS BETWEEN H<sup>∞</sup> AND GENERALLY WEIGHTED BLOCH SPACES ON POLYDISKS

2010-03-23

Haiying Li , Пэйдэ Лю

A NOTE ON NEW ESTIMATES FOR DISTANCES IN ANALYTIC FUNCTION SPACES

2010-02-13

Romi F. Shamoyan , Haiying Li

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Weighted composition operators between generally weighted Bloch spaces of polydisk

2010-01-25

Haiying Li , Пэйдэ Лю

WEIGHTED COMPOSITION OPERATORS BETWEEN H∞ AND GENERALLY WEIGHTED BLOCH SPACES ON POLYDISKS

2010-01-01

Haiying Li , Пэйдэ Лю

Thinking of the retail job of the newspaper and periodicals

2010-01-01

Haiying Li

On a Stevic integral-type operator from generally weighted Bloch spaces to Bloch-type spaces on the unit ball.

2010-01-01

Haiying Li , Tianshui Ma

On the action of differentiation operator in some classes of Nevanlinna-Djrbashian type in the unit disk and polydisk

2009-12-01

Romi F. Shamoyan , Haiying Li

We introduce new area Nevanlinna type spaces in the unit disk and polydisk and study the action of classical operator of differentiation on them. We substantially complement the list of … We introduce new area Nevanlinna type spaces in the unit disk and polydisk and study the action of classical operator of differentiation on them. We substantially complement the list of previously known assertions of this type.

Coauthor	Papers Together
Tianshui Ma	17
Changsen Yang	9
Пэйдэ Лю	5
Romi F. Shamoyan	4
Shuanhong Wang	3
Tao Yang	2
Zhitao Guo	2
Min Sun	1
Cui Wang	1
Peng Zhen Chen	1
Man Jun Shang	1
Tong Lei Yu	1
Xuemei Yang	1
Xiangrun Yang	1
Dequan Yue	1
Lihong Dong	1
Haixia Zhang	1
Tingting Xu	1
Ling Wang	1
Linlin Liu	1
Zhicheng Zhang	1
Wang Yaru	1
Shaoxian Xu	1
Yuchen Jia	1
Yisheng Song	1
Tianyu Xue	1
Yaru Wang	1
Yajuan Wang	1
Fenghui Wang	1
Jie Guo	1
Yang Xiang-zhao	1
Xiangbo Zhang	1
Can Liu	1
Yulian Wu	1
Zhao Wen-zheng	1
Chang Sen Yang	1
Xiang un Yang	1
Maofa Wang	1
Yamei Yang	1
Zhi ao Guo	1
Changsen Yang	1
Changsen Yang	1
Bo Jun Chen	1
Linlin Liu	1
Wang Xing-fang	1

Composition Operators on Spaces of Analytic Functions

2019-03-04

Carl C. Cowen , Barbara D. MacCluer

Introduction Analysis Background A Menagerie of Spaces Some Theorems on Integration Geometric Function Theory in the Disk Iteration of Functions in the Disk The Automorphisms of the Ball Julia-Caratheodory Theory … Introduction Analysis Background A Menagerie of Spaces Some Theorems on Integration Geometric Function Theory in the Disk Iteration of Functions in the Disk The Automorphisms of the Ball Julia-Caratheodory Theory in the Ball Norms Boundedness in Classical Spaces on the Disk Compactness and Essential Norms in Classical Spaces on the Disk Hilbert-Schmidt Operators Composition Operators with Closed Range Boundedness on Hp (BN) Small Spaces Compactness on Small Spaces Boundedness on Small Spaces Large Spaces Boundedness on Large Spaces Compactness on Large Spaces Hilbert-Schmidt Operators Special Results for Several Variables Compactness Revisited Wogen's Theorem Spectral Properties Introduction Invertible Operators on the Classical Spaces on the Disk Invertible Operators on the Classical Spaces on the Ball Spectra of Compact Composition Operators Spectra: Boundary Fixed Point, j'(a)

Compact composition operators on the Bloch space

1995-01-01

Kevin M. Madigan , Alec Matheson

Necessary and sufficient conditions are given for a composition operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi Baseline f equals f o phi"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> … Necessary and sufficient conditions are given for a composition operator <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi Baseline f equals f o phi"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> </mml:mrow> <mml:mi>f</mml:mi> <mml:mo>=</mml:mo> <mml:mi>f</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mtext>o</mml:mtext> </mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">{C_\phi }f = f{\text {o}}\phi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to be compact on the Bloch space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathcal {B}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and on the little Bloch space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B 0"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Weakly compact composition operators on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B 0"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are shown to be compact. If <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi element-of script upper B 0"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>∈</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">\phi \in {\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a conformal mapping of the unit disk <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper D"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {D}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> into itself whose image <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi left-parenthesis double-struck upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\phi (\mathbb {D})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> approaches the unit circle <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper T"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {T}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> only in a finite number of nontangential cusps, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{C_\phi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is compact on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper B 0"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">B</mml:mi> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathcal {B}_0}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. On the other hand if there is a point of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper T intersection phi left-parenthesis double-struck upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">T</mml:mi> </mml:mrow> <mml:mo>∩</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {T} \cap \phi (\mathbb {D})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> at which <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi left-parenthesis double-struck upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">D</mml:mi> </mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">\phi (\mathbb {D})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> does not have a cusp, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript phi"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>C</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{C_\phi }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is not compact.

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Composition operators between generally weighted Bloch spaces and $Q_{log}^q$ space

2009-01-01

Haiying Li , Пэйдэ Лю

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Spaces of Holomorphic Functions in the Unit Ball

2005-01-01

Kehe Zhu

Hopf Algebras and Their Actions on Rings

1993-10-28

Susan Montgomery

Definitions and examples Integrals and semisimplicity Freeness over subalgebras Action of finite-dimensional Hopf algebras and smash products Coradicals and filtrations Inner actions Crossed products Galois extensions Duality New constructions from … Definitions and examples Integrals and semisimplicity Freeness over subalgebras Action of finite-dimensional Hopf algebras and smash products Coradicals and filtrations Inner actions Crossed products Galois extensions Duality New constructions from quantum groups Some quantum groups.

COMPOSITION OPERATORS BETWEEN GENERALLY WEIGHTED BLOCH SPACES OF POLYDISK

2007-01-01

Haiying Li , Пэйдэ Лю , Maofa Wang

The composition operators on weighted Bloch space

2002-04-01

Rikio Yoneda

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Semi-direct products of Hopf algebras

1977-07-01

Richard K. Molnar

Generalized composition operators on Zygmund spaces and Bloch type spaces

2007-06-21

Songxiao Li , Stevo Stević

Wheeling around von Neumann–Jordan constant in Banach spaces

2008-01-01

José M. Alonso , Pedro Martín , Pier Luigi Papini

In recent times, many constants in Banach spaces have been defined and//or studied. Relations and inequalities among them (sometimes very complicated) have been indicated. But not much effort has been … In recent times, many constants in Banach spaces have been defined and//or studied. Relations and inequalities among them (sometimes very complicated) have been indicated. But not much effort has been devoted to organize all connections, also because the

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Monoidal Hom–Hopf Algebras

2011-06-01

S. Caenepeel , Isar Goyvaerts

Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a … Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras, and Lie algebras.

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An inequality between Jordan–von Neumann constant and James constant

2009-10-10

Changsen Yang , Haiying Li

Compact composition operators on the Bloch space in polydiscs

2001-03-01

Ze‐Hua Zhou , Jihuai Shi

On James and von Neumann–Jordan constants and sufficient conditions for the fixed point property

2005-12-16

Satit Saejung

On the classification of finite-dimensional pointed Hopf algebras

2010-03-17

Nicolás Andruskiewitsch , Hans‐Jürgen Schneider

We classify finite-dimensional complex Hopf algebras A which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements G.A/ is abelian such that … We classify finite-dimensional complex Hopf algebras A which are pointed, that is, all of whose irreducible comodules are one-dimensional, and whose group of group-like elements G.A/ is abelian such that all prime divisors of the order of G.A/ are > 7. Since these Hopf algebras turn out to be deformations of a natural class of generalized small quantum groups, our result can be read as an axiomatic description of generalized small quantum groups. Ã pointed % nonsemisimple & otherIf A D A 0 , then A is semisimple as an algebra.Semisimple Hopf algebras define examples of fusion categories.There are various important results

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Crossed products by a coalgebra

1997-01-01

Tomasz Brzeziński

Abstract We introduce the notion of a crossed product of an al¬gebra by a coalgebra C, which generalises the notion of a crossed product by a bialgebra well-studied in the … Abstract We introduce the notion of a crossed product of an al¬gebra by a coalgebra C, which generalises the notion of a crossed product by a bialgebra well-studied in the theory of Hopf algebras. The result of such a crossed product is an algebra which is also a right C-comodule. We find the necessary and sufficient conditions for two coalgebra crossed products be equivalent. We show that the two-dimensional quantum Euclidean group is a coalgebra crossed product. The paper is completed with an appendix describing the dualisation of construction of coalgebra crossed products.

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Hom-quantum groups II: cobraided Hom-bialgebras and Hom-quantum geometry

2009-01-01

Donald Yau

A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several methods for … A class of non-associative and non-coassociative generalizations of cobraided bialgebras, called cobraided Hom-bialgebras, is introduced. The non-(co)associativity in a cobraided Hom-bialgebra is controlled by a twisting map. Several methods for constructing cobraided Hom-bialgebras are given. In particular, Hom-type generalizations of FRT quantum groups, including quantum matrices and related quantum groups, are obtained. Each cobraided Hom-bialgebra comes with solutions of the operator quantum Hom-Yang-Baxter equations, which are twisted analogues of the operator form of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from comodules of suitable cobraided Hom-bialgebras. Hom-type generalizations of the usual quantum matrices coactions on the quantum planes give rise to non-associative and non-coassociative analogues of quantum geometry.

Braided bialgebras and quadratic blalgebras

1993-01-01

Yukio Doi

(1993). Braided bialgebras and quadratic blalgebras. Communications in Algebra: Vol. 21, No. 5, pp. 1731-1749. (1993). Braided bialgebras and quadratic blalgebras. Communications in Algebra: Vol. 21, No. 5, pp. 1731-1749.

On James and Jordan–von Neumann Constants of Lorentz Sequence Spaces

2001-06-01

Mikio Kato , Lech Maligranda

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The Von Neumann-Jordan Constant for the Lebesgue Spaces

1937-01-01

James A. Clarkson

On two classes of Banach spaces with uniform normal structure

1991-01-01

Ji Gao , Ka‐Sing Lau

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On James and Jordan–von Neumann constants and the normal structure coefficient of Banach spaces

2001-01-01

Mikio Kato , Lech Maligranda , Yasuji Takahashi

Some relations between the James (or non-square) constant $J(X)$ and the Jordan–von Neumann constant $C_{\rm NJ}(X)$, and the normal structure coefficient $N(X)$ of Banach spaces $X$ are investigated. Relations between … Some relations between the James (or non-square) constant $J(X)$ and the Jordan–von Neumann constant $C_{\rm NJ}(X)$, and the normal structure coefficient $N(X)$ of Banach spaces $X$ are investigated. Relations between $J(X)$ and $J(X^*)$ are given

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The Order of the Antipode of Finite-dimensional Hopf Algebra

1971-11-01

Earl J. Taft

Examples of finite-dimensional Hopf algebras over a field, whose antipodes have arbitrary even orders ≥4 as mappings, are furnished. The dimension of the Hopf algebra is q n +1 , … Examples of finite-dimensional Hopf algebras over a field, whose antipodes have arbitrary even orders ≥4 as mappings, are furnished. The dimension of the Hopf algebra is q n +1 , where the antipode has order 2 q , q ≥ 2, and n is an arbitrary positive integer. The algebras are not semisimple, and neither they nor their dual algebras are unimodular.

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HOM-ALGEBRAS AND HOM-COALGEBRAS

2010-04-09

Abdenacer Makhlouf , Sergei Silvestrov

The aim of this paper is to develop the theory of Hom-coalgebras and related structures. After reviewing some key constructions and examples of quasi-deformations of Lie algebras involving twisted derivations … The aim of this paper is to develop the theory of Hom-coalgebras and related structures. After reviewing some key constructions and examples of quasi-deformations of Lie algebras involving twisted derivations and giving rise to the class of quasi-Lie algebras incorporating Hom–Lie algebras, we describe the notion and some properties of Hom-algebras and provide examples. We introduce Hom-coalgebra structures, leading to the notions of Hom-bialgebra and Hom–Hopf algebras, and prove some fundamental properties and give examples. Finally, we define the concept of Hom–Lie admissible Hom-coalgebra and provide their classification based on subgroups of the symmetric group.

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Hom-quantum groups III: Representations and module Hom-algebras

2009-01-01

Donald Yau

We study Hom-quantum groups, their representations, and module Hom-algebras. Two Twisting Principles for Hom-type algebras are formulated, and construction results are proved following these Twisting Principles. Examples include Hom-quantum n-spaces, … We study Hom-quantum groups, their representations, and module Hom-algebras. Two Twisting Principles for Hom-type algebras are formulated, and construction results are proved following these Twisting Principles. Examples include Hom-quantum n-spaces, Hom-quantum enveloping algebras of Kac-Moody algebras, Hom-Verma modules, and Hom-type analogs of U_q(sl_2)-module-algebra structures on the quantum planes.

The Hom–Yang–Baxter equation and Hom–Lie algebras

2011-05-01

Donald Yau

Motivated by recent work on Hom–Lie algebras, a twisted version of the Yang–Baxter equation, called the Hom–Yang–Baxter equation (HYBE), was introduced by Yau [J. Phys. A 42, 165202 (2009)]. In … Motivated by recent work on Hom–Lie algebras, a twisted version of the Yang–Baxter equation, called the Hom–Yang–Baxter equation (HYBE), was introduced by Yau [J. Phys. A 42, 165202 (2009)]. In this paper, several more classes of solutions of the HYBE are constructed. Some of the solutions of the HYBE are closely related to the quantum enveloping algebra of \documentclass[12pt]{minimal}\begin{document}$\mathfrak {sl}(2)$\end{document}sl(2), the Jones–Conway polynomial, and Yetter-Drinfel'd modules. Under some invertibility conditions, we construct a new infinite sequence of solutions of the HYBE from a given one.

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On n-th James and Khintchine constants of Banach spaces

2008-01-01

Lech Maligranda , Ludmila Nikolova , Lars‐Erik Persson +1 more

For any Banach space X the n -th James constants J n (X) and the n -th Khintchine constants K n p,q (X) are investigated and discussed.Some new properties of … For any Banach space X the n -th James constants J n (X) and the n -th Khintchine constants K n p,q (X) are investigated and discussed.Some new properties of these constants are presented.The main result is an estimate of the n -th Khintchine constants K n p,q (X) by the n -th James constants J n (X) .In the case of n = 2 and p = q = 2 this estimate is even stronger and improvs an earlier estimate proved by .

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Cobraided smash product Hom-Hopf algebras

2014-01-01

Tianshui Ma , Haiying Li , Tao Yang

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A Volterra Type Operator on Spaces of Analytic Functions

1999-01-01

Aristomenis G Sisakis , Ruhan Zhao

Composition Operators on the Bloch Space of Several Complex Variables

2000-01-01

Jihuai Shi , Luo Luo

Generalised Jordan-von Neumann constants and uniform normal structure

2003-04-01

Sompong Dhompongsa , P. Piraisangjun , Satit Saejung

We introduce a new geometric coefficient related to the Jordan-von Neumann constant. This leads to improved versions of known results and yields new ones on super-normal structure for Banach spaces. We introduce a new geometric coefficient related to the Jordan-von Neumann constant. This leads to improved versions of known results and yields new ones on super-normal structure for Banach spaces.

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Hom-algebra structures

2008-01-01

Abdenacer Makhlouf , Sergei Silvestrov

Hom-algebra structures are given on linear spaces by multiplications twisted by linear maps. Hom-Lie algebras and general quasi-Hom-Lie and quasi-Lie algebras were introduced by Hartwig, Larsson and Silvestrov as algebras … Hom-algebra structures are given on linear spaces by multiplications twisted by linear maps. Hom-Lie algebras and general quasi-Hom-Lie and quasi-Lie algebras were introduced by Hartwig, Larsson and Silvestrov as algebras embracing Lie algebras, super and color Lie algebras and their quasi-deformations by twisted derivations. In this paper we introduce and study Hom-associative, Hom-Leibniz and Hom-Lie admissible algebraic structures generalizing associative, Leibniz and Lie admissible algebras. Also, we characterize flexible Hom-algebras and explain some connections and differences between Hom-Lie algebras and Santilli’s isotopies of associative and Lie algebras.

On the geometry of spheres in normed linear spaces

1990-02-01

Ji Gao , Ka‐Sing Lau

Abstract Some simplifications of Schäffer's girth and perimeter of the unit spheres are introduced. Their general properties are discussed, and they are used to study the l p , L … Abstract Some simplifications of Schäffer's girth and perimeter of the unit spheres are introduced. Their general properties are discussed, and they are used to study the l p , L p spaces, uniformly nonsquare spaces, and their isomorphic classes.

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Weighted Composition Operators between Bloch-Type Spaces

2003-03-01

Shûichi Ohno , Karel Stroethoff , Ruhan Zhao

We discuss boundedness and compactness of composition operators followed by multiplication as operators between Bloch-type spaces of analytic functions on the unit disk. We discuss boundedness and compactness of composition operators followed by multiplication as operators between Bloch-type spaces of analytic functions on the unit disk.

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Weighted Composition Operators Between Zygmund Type Spaces and Their Essential Norms

2013-02-11

Kobra Esmaeili , Mikael Lindström

The structure of Hopf algebras with a projection

1985-02-01

David E. Radford

On a new geometric constant related to the von Neumann–Jordan constant

2006-01-19

Changsen Yang , Fenghui Wang

ON CROSSED DOUBLE BIPRODUCT

2012-10-02

Tianshui Ma , Zhengming Jiao , Yanan Song

Let H be a bialgebra. Let σ : H ⊗ H → A be a linear map, where A is a left H-comodule coalgebra, and an algebra with a left … Let H be a bialgebra. Let σ : H ⊗ H → A be a linear map, where A is a left H-comodule coalgebra, and an algebra with a left H-weak action. Let B be a right H-module algebra and also a comodule coalgebra. In this paper, we provide necessary and sufficient conditions for the one-sided crossed product algebra A# σ H # B and the two-sided smash coproduct coalgebra A × H × B to form a bialgebra, which we call the crossed double biproduct. Majid's double biproduct is recovered from this. Moreover, necessary and sufficient conditions are given for Brzeziński's crossed product equipped with the smash coproduct coalgebra structure to be a bialgebra. The celebrated Radford's biproduct in [The structure of Hopf algebra with a projection, J. Algebra92 (1985) 322–347], the unified product defined by Agore and Militaru in [Extending structures II: The quantum version, J. Algebra336 (2011) 321–341] and the Wang–Jiao–Zhao's crossed product in [Hopf algebra structures on crossed products Comm. Algebra26 (1998) 1293–1303] are all derived as special cases.

GENERALIZED COMPOSITION OPERATORS FROM GENERALIZED WEIGHTED BERGMAN SPACES TO BLOCH TYPE SPACES

2009-11-01

Xiangling Zhu

Let H(B) denote the space of all holomorphic functions on the unit ball B of <TEX>$\mathbb{C}^n$</TEX>. Let <TEX>$\varphi$</TEX> = (<TEX>${\varphi}_1,{\ldots}{\varphi}_n$</TEX>) be a holomorphic self-map of B and <TEX>$g{\in}2$</TEX>(B) with g(0) … Let H(B) denote the space of all holomorphic functions on the unit ball B of <TEX>$\mathbb{C}^n$</TEX>. Let <TEX>$\varphi$</TEX> = (<TEX>${\varphi}_1,{\ldots}{\varphi}_n$</TEX>) be a holomorphic self-map of B and <TEX>$g{\in}2$</TEX>(B) with g(0) = 0. In this paper we study the boundedness and compactness of the generalized composition operator <TEX>$C_{\varphi}^gf(z)=\int_{0}^{1}{\mathfrak{R}}f(\varphi(tz))g(tz){\frac{dt}{t}}$</TEX> from generalized weighted Bergman spaces into Bloch type spaces.

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Weighted radial operator from the mixed-norm space to the nth weighted-type space on the unit ball

2012-03-30

Stevo Stević

Bounded mean oscillation of Bloch pull-backs

1991-03-01

Wade Ramey , David Ullrich

On an integral-type operator from logarithmic Bloch-type spaces to mixed-norm spaces on the unit ball

2009-11-28

Stevo Stević

On the braided structures of Radford's biproduct

2011-03-01

Tianshui Ma , Haiying Li , Zhao Wen-zheng

Bitwistor and Quasitriangular Structures of Bialgebras

2010-08-31

Tianshui Ma , Shuanhong Wang

In this article, we first introduce the notion of a bitwistor and discuss conditions under which such bitwistor forms a bialgebra as a generalization of the well-known Radford's biproduct. Then, … In this article, we first introduce the notion of a bitwistor and discuss conditions under which such bitwistor forms a bialgebra as a generalization of the well-known Radford's biproduct. Then, in order to obtain new quasitriangular bialgebras, we consider a construction called twisted tensor biproduct, which is a special case of bitwistor bialgebra, and give a necessary and sufficient condition for such twisted tensor biproduct to admit quasitriangular structures.

Hom-quantum groups: I. Quasi-triangular Hom-bialgebras

2012-01-19

Donald Yau

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting … We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel'd's quasi-triangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel'd's quantum enveloping algebras. Each quasi-triangular Hom-bialgebra comes with a solution of the quantum Hom-Yang-Baxter equation, which is a non-associative version of the quantum Yang-Baxter equation. Solutions of the Hom-Yang-Baxter equation can be obtained from modules of suitable quasi-triangular Hom-bialgebras.

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Integrals for monoidal Hom-Hopf algebras and their applications

2013-07-01

Yuanyuan Chen , Zhongwei Wang , Liangyun Zhang

Integrals of monoidal Hom-Hopf algebras are introduced and the existence and uniqueness of integrals for finite-dimensional monoidal Hom-Hopf algebras are investigated first. Then integrals are applied to the Maschke type … Integrals of monoidal Hom-Hopf algebras are introduced and the existence and uniqueness of integrals for finite-dimensional monoidal Hom-Hopf algebras are investigated first. Then integrals are applied to the Maschke type theorem for monoidal Hom-Hopf algebras controlling the semisimplicity and separability of monoidal Hom-Hopf algebras. Further, monoidal Hom-algebras are characterized with additional Frobenius property, and the question when finite-dimensional monoidal Hom-Hopf algebras are Frobenius is studied. As applications of integrals, the Maschke type theorem for Hom-smash product is given, and the Morita context in the Hom-category \documentclass[12pt]{minimal}\begin{document}$\widetilde{\mathcal {H}}(\mathcal {M}_k)$\end{document}H̃(Mk) is constructed.

Crossed products and inner actions of Hopf algebras

1986-01-01

Robert J. Blattner , Miriam Cohen , Susan Montgomery

This paper develops a theory of crossed products and inner (weak) actions of arbitrary Hopf algebras on noncommutative algebras. The theory covers the usual examples of inner automorphisms and derivations, … This paper develops a theory of crossed products and inner (weak) actions of arbitrary Hopf algebras on noncommutative algebras. The theory covers the usual examples of inner automorphisms and derivations, and in addition is general enough to include "inner" group gradings of algebras. We prove that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi colon upper H right-arrow upper H overbar"> <mml:semantics> <mml:mrow> <mml:mi>π</mml:mi> <mml:mo>:</mml:mo> <mml:mi>H</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mover> <mml:mi>H</mml:mi> <mml:mo accent="false">¯</mml:mo> </mml:mover> </mml:mrow> <mml:annotation encoding="application/x-tex">\pi :H \to \overline H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a Hopf algebra epimorphism which is split as a coalgebra map, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is algebra isomorphic to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A number-sign Subscript sigma Baseline upper H"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi mathvariant="normal">#</mml:mi> <mml:mi>σ</mml:mi> </mml:msub> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">A{\# _\sigma }H</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, a crossed product of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with the left Hopf kernel <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding="application/x-tex">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="pi"> <mml:semantics> <mml:mi>π</mml:mi> <mml:annotation encoding="application/x-tex">\pi</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Given any crossed product <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A number-sign Subscript sigma Baseline upper H"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi mathvariant="normal">#</mml:mi> <mml:mi>σ</mml:mi> </mml:msub> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">A{\# _\sigma }H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (weakly) inner on <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding="application/x-tex">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A number-sign Subscript sigma Baseline upper H"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi mathvariant="normal">#</mml:mi> <mml:mi>σ</mml:mi> </mml:msub> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">A{\# _\sigma }H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is isomorphic to a twisted product <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Subscript tau Baseline left-bracket upper H right-bracket"> <mml:semantics> <mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>A</mml:mi> <mml:mi>τ</mml:mi> </mml:msub> </mml:mrow> <mml:mo stretchy="false">[</mml:mo> <mml:mi>H</mml:mi> <mml:mo stretchy="false">]</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">{A_\tau }[H]</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with trivial action. Finally, if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a finite dimensional semisimple Hopf algebra, we consider when semisimplicity or semiprimeness of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A"> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding="application/x-tex">A</mml:annotation> </mml:semantics> </mml:math> </inline-formula> implies that of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A number-sign Subscript sigma Baseline upper H"> <mml:semantics> <mml:mrow> <mml:mi>A</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi mathvariant="normal">#</mml:mi> <mml:mi>σ</mml:mi> </mml:msub> </mml:mrow> <mml:mi>H</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">A{\# _\sigma }H</mml:annotation> </mml:semantics> </mml:math> </inline-formula>; in particular this is true if the (weak) action of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is inner.