In this paper, we firstly establish new numerical radius inequalities which refine a result of Kittaneh in [Studia Math. 168, 73–80 (2005)], then present some numerical radius inequalities involving non-negative …
In this paper, we firstly establish new numerical radius inequalities which refine a result of Kittaneh in [Studia Math. 168, 73–80 (2005)], then present some numerical radius inequalities involving non-negative increasing convex functions for n×n operator matrices, which generalize the related results of Shebrawi in [Linear Algebra Appl. 523(15), 1–12 (2017)].
We prove a numerical radius inequality for operator matrices, which improves an earlier inequality due to Hou and Du. As an application of this numerical radius inequality, we derive a …
We prove a numerical radius inequality for operator matrices, which improves an earlier inequality due to Hou and Du. As an application of this numerical radius inequality, we derive a new bound for the zeros of polynomials.
We present upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices which improves on the existing bound for the same. As an application of the …
We present upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices which improves on the existing bound for the same. As an application of the results obtained we give a better estimation for the zeros of a polynomial.
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms …
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators. Moreover, operator matrices with positive real and imaginary parts will be discussed, and sharper bounds will be shown for such classes.
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms …
Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators. Moreover, operator matrices whose real and imaginary parts are positive will be discussed, and sharper bounds will be shown for such class.
This paper is a continuation of a recent work on a new norm, christened the $ (\alpha, \beta)$-norm, on the space of bounded linear operators on a Hilbert space. We …
This paper is a continuation of a recent work on a new norm, christened the $ (\alpha, \beta)$-norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of $n\times n$ operator matrices. As an application of the present study, we estimate bounds for the numerical radius and the usual operator norm of $n\times n$ operator matrices, which generalize the existing ones.
The aim of this article is to prove several new numerical radius inequalities for n × n operator matrices on a Hilbert space. Let H1,H2,…, Hn be complex Hilbert spaces, …
The aim of this article is to prove several new numerical radius inequalities for n × n operator matrices on a Hilbert space. Let H1,H2,…, Hn be complex Hilbert spaces, and let T=[Tij] be an n × n operator matrix with Tij∈B(Hj,Hi). Among other inequalities, it shown thatω(T)≤12∑i=1n(w(Tii)+ω2(Tii)+∑j=1j≠in||Tij||2),where ω(·) and ||·|| denote the numerical radius and the usual operator norm, respectively.
We prove a generalized numerical radius inequality for operator matrices, which improves and generalized an earlier inequality due to BaniDomi and Kittaneh.
We prove a generalized numerical radius inequality for operator matrices, which improves and generalized an earlier inequality due to BaniDomi and Kittaneh.
Abstract Let A i ∈ B ( H ), ( i = 1, 2, ..., n ), and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>T</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mtable> <m:mtr> <m:mtd> <m:mn>0</m:mn> …
Abstract Let A i ∈ B ( H ), ( i = 1, 2, ..., n ), and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>T</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mo>[</m:mo> <m:mrow> <m:mtable> <m:mtr> <m:mtd> <m:mn>0</m:mn> </m:mtd> <m:mtd> <m:mo>⋯</m:mo> </m:mtd> <m:mtd> <m:mn>0</m:mn> </m:mtd> <m:mtd> <m:mrow> <m:msub> <m:mi>A</m:mi> <m:mn>1</m:mn> </m:msub> </m:mrow> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mo>⋮</m:mo> </m:mtd> <m:mtd> <m:mo>⋰</m:mo> </m:mtd> <m:mtd> <m:mrow> <m:msub> <m:mi>A</m:mi> <m:mn>2</m:mn> </m:msub> </m:mrow> </m:mtd> <m:mtd> <m:mn>0</m:mn> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mn>0</m:mn> </m:mtd> <m:mtd> <m:mo>⋰</m:mo> </m:mtd> <m:mtd> <m:mo>⋰</m:mo> </m:mtd> <m:mtd> <m:mo>⋮</m:mo> </m:mtd> </m:mtr> <m:mtr> <m:mtd> <m:mrow> <m:msub> <m:mi>A</m:mi> <m:mi>n</m:mi> </m:msub> </m:mrow> </m:mtd> <m:mtd> <m:mn>0</m:mn> </m:mtd> <m:mtd> <m:mo>⋯</m:mo> </m:mtd> <m:mtd> <m:mn>0</m:mn> </m:mtd> </m:mtr> </m:mtable> </m:mrow> <m:mo>]</m:mo> </m:mrow> </m:mrow> </m:math> $ T = \left[ {\matrix{ 0 & \cdots & 0 & {A_1 } \cr \vdots & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {A_2 } & 0 \cr 0 & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & {\mathinner{\mkern2mu\raise1pt\hbox{.}\mkern2mu \raise4pt\hbox{.}\mkern2mu\raise7pt\hbox{.}\mkern1mu}} & \vdots \cr {A_n } & 0 & \cdots & 0 \cr } } \right] $ . In this paper, we present some upper bounds and lower bounds for w ( T ). At the end of this paper we drive a new bound for the zeros of polynomials.
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we …
We completely characterize Birkhoff-James orthogonality with respect to numerical radius norm in the space of bounded linear operators on a complex Hilbert space. As applications of the results obtained, we estimate lower bounds of numerical radius for $n\times n$ operator matrices, which improve on and generalize existing lower bounds. We also obtain a better lower bound of numerical radius for an upper triangular operator matrix.
We derive several numerical radius inequalities for $2\times 2 $ operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.
We derive several numerical radius inequalities for $2\times 2 $ operator matrices. Numerical radius inequalities for sums and products of operators are given. Applications of our inequalities are also provided.
The concepts of weighted numerical radius has been defined in recent times. In this article, we obtain several upper bound for weighted numerical radius of operators and $2 \times 2$ …
The concepts of weighted numerical radius has been defined in recent times. In this article, we obtain several upper bound for weighted numerical radius of operators and $2 \times 2$ operator matrices which generalize and improves some well known famous inequality for classical numerical radius. We also obtain an upper bound for the weighted numerical radius of the Aluthge transformation, $\tilde{T}$ of an operator $T \in \mathcal{B}(\mathcal{H}),$ where $\tilde{T} = |T|^{1/2} U |T|^{1/2}$ and $T = U |T|$ be the canonical polar decomposition of $T.$
A general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and …
A general inequality involving powers of the numerical radius for sums and products of Hilbert space operators is given. This inequality generalizes several recent inequalities for the numerical radius, and includes that if and are operators on a complex Hilbert space , then for . It is also shown that if is normal , then . Related numerical radius and usual operator norm inequalities for sums and products of operators are also presented.
Several upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices are developed which refine and generalize the earlier related bounds. In particular, we show that …
Several upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices are developed which refine and generalize the earlier related bounds. In particular, we show that if $B,C$ are bounded linear operators on a complex Hilbert space, then \begin{eqnarray*} && \frac{1}{2}\max \left \{ \|B\|, \|C\| \right \}+\frac{1}{4} \left | \|B+C^*\|-\|B-C^*\| \right | &&\leq w \left(\left[\begin{array}{cc} 0 & B C& 0 \end{array}\right]\right)\\ &&\leq \frac{1}{2} \max \left\{\|B\|,\|C\|\right \}+\frac{1}{2}\max \left \{r^{\frac{1}{2}}(|B||C^*|),r^{\frac{1}{2}}(|B^*||C|)\right\}, \end{eqnarray*} where $w(.)$, $r(.)$ and $\|.\|$ are the numerical radius, spectral radius and operator norm of a bounded linear operator, respectively. We also obtain equality conditions for the numerical radius of the operator matrix $\left[\begin{array}{cc} 0 & B C& 0 \end{array}\right]$. As application of results obtained, we show that if $B,C$ are self-adjoint operators then, $\max \Big \{\|B+C\|^2 , \|B-C\|^2 \Big\}\leq \left \|B^2+C^2 \right \|+2w(|B||C|). $
In this paper we prove some upper and lower bounds for the numerical radius of the off-diagonal part of 3 X 3 operator matrices and some bounds for the numerical …
In this paper we prove some upper and lower bounds for the numerical radius of the off-diagonal part of 3 X 3 operator matrices and some bounds for the numerical radius inequalities of the general 3 X 3 operator matrix.
We prove a numerical radius inequality for operator matrices, which improves an earlier inequality due to Hou and Du. As an application of this numerical radius inequality, we derive a …
We prove a numerical radius inequality for operator matrices, which improves an earlier inequality due to Hou and Du. As an application of this numerical radius inequality, we derive a new bound for the zeros of polynomials.
Several inequalities for Hilbert space operators are extended. These include results of Furuta, Halmos, and Kato on the mixed Schwarz inequality, the generalized Reid inequality as proved by Halmos and …
Several inequalities for Hilbert space operators are extended. These include results of Furuta, Halmos, and Kato on the mixed Schwarz inequality, the generalized Reid inequality as proved by Halmos and a classical inequality in the theory of compact non-self-adjoint operators which is essentially due to Weyl. Some related inequalities are also discussed.
It is shown that if $A$ is a bounded linear operator on a complex Hilbert space, then $$ w(A) \le \frac{1}{2} (\| A \| + \| A^2 \|^{1/2} ), $$ …
It is shown that if $A$ is a bounded linear operator on a complex Hilbert space, then $$ w(A) \le \frac{1}{2} (\| A \| + \| A^2 \|^{1/2} ), $$ where $w(A)$ and $\|A\|$ are the numerical radius and the usual operator norm of $A$, respectively. An applicati
We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of n×n …
We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of n×n operator matrices by using non-negative continuous functions on [0,∞). We also obtain some upper and lower bounds for the B-numerical radius of operator matrices, where B is the diagonal operator matrix whose each diagonal entry is a positive operator A. We show that these bounds generalize and improve on the existing bounds.
We present upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices which improves on the existing bound for the same. As an application of the …
We present upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices which improves on the existing bound for the same. As an application of the results obtained we give a better estimation for the zeros of a polynomial.
It is shown that if $A$ is a bounded linear operator on a complex Hilbert space, then $$ {1 \over 4}\| {A^* A + AA^* } \| \le ( {w(A …
It is shown that if $A$ is a bounded linear operator on a complex Hilbert space, then $$ {1 \over 4}\| {A^* A + AA^* } \| \le ( {w(A )} )^2 \le {1 \over 2}\| {A^* A + AA^* }\| , $$ where $w(\cdot )$ and $\| \cdot \| $ are the numerical radius and the u
In this paper, we discuss and present new sharp inequalities for the numerical radii of Hilbert space operators. In particular, if A and B are bounded linear operators on a …
In this paper, we discuss and present new sharp inequalities for the numerical radii of Hilbert space operators. In particular, if A and B are bounded linear operators on a Hilbert space, we present new upper bounds for ω(A∗B). The main tool to obtain our results is using block matrix techniques. Among many interesting results, and as an application of the new inequalities, we obtain the following bound for the numerical radius of an operator T, ω(T)≤12(‖T‖1/2‖|T|1/2+|T∗|1/2‖),where ω(⋅), ‖⋅‖, and |⋅| denote the numerical radius, the usual operator norm, and the absolute value operator, respectively. Other difference inequalities will be presented too.