Takayuki Furuta

Generating author description...

All published works

Action	Title	Year	Authors
+ PDF Chat	Upper and lower bounds, and operator monotonicity of an extension of the Petz-Hasegawa function	2017	Takayuki Furuta Masatoshi Ito Takeaki Yamazaki Masahiro Yanagida
+ PDF Chat	Upper and lower bounds, and operator monotonicity of an extension of the Petz-Hasegawa function	2017	Takayuki Furuta Masatoshi Ito Takeaki Yamazaki Masahiro Yanagida
+ PDF Chat	Precise lower bound of f(A)-f(B) for A>B>0 and non-constant operator monotone function f on [0,∞)	2015	Takayuki Furuta
+	Comprehensive survey on an order preserving operator inequality	2013	Takayuki Furuta
+ PDF Chat	Operator monotone functions, A >B > 0 and logA > logB	2013	Takayuki Furuta
+	Elementary Proof of Petz–Hasegawa Theorem	2012	Takayuki Furuta
+	OPERATOR FUNCTIONS ON CHAOTIC ORDER INVOLVING ORDER PRESERVING OPERATOR INEQUALITIES (Structural study of operators via spectra or numerical ranges)	2012	Takayuki Furuta
+	Extensions of inequalities for unitarily invariant norms via log majorization	2012	Takayuki Furuta
+ PDF Chat	Operator functions on chaotic order involving order preserving operator inequalities	2012	Takayuki Furuta
+	ASYMMETRIC VARIATION OF CHOI INEQUALITY FOR POSITIVE LINEAR MAP (Noncommutative Structure in Operator Theory and its Application)	2011	Takayuki Furuta
+	Around Choi inequalities for positive linear maps	2010	Takayuki Furuta
+	Operator equations via an order preserving operator inequality (Prospects of non-commutative analysis in operator theory)	2010	Takayuki Furuta
+ PDF Chat	An extension of order preserving operator inequality	2010	Takayuki Furuta
+	Positive semidefinite solutions of the operator equation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msubsup><mml:mrow><mml:mo>∑</mml:mo></mml:mrow><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>-</mml:mo><mml:mi>j</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:…	2009	Takayuki Furuta
+	Log majorization via an order preserving operator inequality	2009	Takayuki Furuta
+	Further extension of an order preserving operator inequality and its application (Application of Geometry to Operator Theory)	2009	Takayuki Furuta
+ PDF Chat	Operator function associated with an order preserving operator inequality	2009	Takayuki Furuta
+	BRIEF SURVEY OF RECENT APPLICATIONS OF AN ORDER PRESERVING OPERATOR INEQUALITY	2008	Takayuki Furuta
+ PDF Chat	BRIEF SURVEY OF RECENT APPLICATIONS OF AN ORDER PRESERVING OPERATOR INEQUALITY	2008	Takayuki Furuta
+	$A \ge B \ge 0$ ensures $(A^{\frac{r}{2}}A^pA^{\frac{r}{2}})^{\frac{1}{q}} \ge (A^{\frac{r}{2}}B^pA^{\frac{r}{2}})^{\frac{1}{q}}$ for $p \ge 0,q \ge 1,r \ge 0$ with $(1+r)q \ge p+r$ and brief survey of its recent applications (Inequalities on Linear Operators and its Applications)	2008	Takayuki Furuta
+ PDF Chat	Further extension of an order preserving operator inequality	2008	Takayuki Furuta
+	Applications of polar decompositions of idempotent and 2-nilpotent operators	2007	Takayuki Furuta
+	Monotonicity of order preserving operator functions	2007	Takayuki Furuta
+	Operator inequality implying generalized Bebiano–Lemos–Providência one	2007	Takayuki Furuta
+	Concrete examples of operator monotone functions obtained by an elementary method without appealing to Löwner integral representation	2007	Takayuki Furuta
+	REVERSE INEQUALITIES ASSOCIATED WITH TSALLIS RELATIVE OPERATOR ENTROPY VIA GENERALIZED KANTOROVICH CONSTANT(Recent Developments in Linear Operator Theory and its Applications)	2005	Takayuki Furuta
+	Reverse inequalities involving two relative operator entropies and two relative entropies (Advanced Study of Applied Functional Analysis and Information Sciences)	2005	Takayuki Furuta
+	Two reverse inequalities associated with Tsallis relative operator entropy via generalized Kantorovich constant and their applications	2005	Takayuki Furuta
+	Reverse inequalities involving two relative operator entropies and two relative entropies	2005	Takayuki Furuta
+	Logarithmic trace inequalities (Role of Operator Inequalities in Operator Theory)	2005	Takayuki Furuta
+ PDF Chat	Short proof that the arithmetic mean is greater than the harmonic mean and its reverse inequality	2005	Takayuki Furuta
+	Mond-Pecaric Method in Operator Inequalities	2005	Takayuki Furuta Jadranka Mičić ‎Josip Pečarić Yūki Seo
+	A counterexample to the question proposed by Yanagi–Furuichi–Kuriyama on matrix inequalities and related counterexamples	2004	Takayuki Furuta
+	Convergence of logarithmic trace inequalities via generalized Lie–Trotter formulae	2004	Takayuki Furuta
+	Generalization of operator type Shannon inequality and its reverse one (Advanced Topics of Information Science and Functional Analysis)	2004	Takayuki Furuta
+	Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators via characterizations of operator concave functions (Recent Topics on Operator inequalities)	2004	Takayuki Furuta
+	Positive Operator Majorization and p -hyponormality	2004	Takayuki Furuta Jung Il Bong Lambert Alan
+	Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators	2004	Takayuki Furuta
+	Order preserving inequalities and related operator functions	2004	Takayuki Furuta Mariko Giga
+	Operator inequalities associated with AlogA via Specht ratio	2003	Takayuki Furuta
+	Specht ratio &S(1)& can be expressed by generalized Kantorovich constant &K(p)&: &S(1)& = &e^{K^{\prime}(1)}& and its application to operator inequalities associated with A log A (Structure of operators and related current topics)	2003	Takayuki Furuta
+	A complementary result of Kantorovich type order preserving inequalities by Mićić–Pečarić–Seo	2003	Takayuki Furuta Mariko Giga
+ PDF Chat	Simple proof of jointly concavity of the relative operator entropy S(A\|B) = A^1/2 log (A^-1/2 BA^-1/2) A^1/2	2003	Takayuki Furuta Mariko Giga Masahiro Yanagida
+ PDF Chat	Specht ratio S(1) can be expressed by Kantorovich constant K(p) : S(1)= exp[K'(1)] and its application	2003	Takayuki Furuta
+ PDF Chat	An operator inequality associated with the operator concavity of operator entropy A log A^-1	2003	Takayuki Furuta ‎Josip Pečarić
+	Some topics on order preserving operator inequalities (Current topics on operator theory and operator inequalities)	2002	Takayuki Furuta
+ PDF Chat	A proof of an order preserving inequality	2002	Takayuki Furuta
+	An operator monotone function tlogt−t+1log2t and strictly chaotic order	2002	Takayuki Furuta
+ PDF Chat	An extension of Uchiyama's result associated with an order preserving operator inequality	2002	Takayuki Furuta Eizaburo Kamei
+	Invitation to Linear Operators	2001	Takayuki Furuta
+	A 【greater than or equal】 B 【greater than or equal】 0 ENSURES (A^ A^p A^ )^ 【greater than or equal】 (A^ B^p A )^ FOR p 【greater than or equal】 0, q 【greater than or equal】 1, r 【greater than or equal】 0 WITH (1+r)q 【greater than or equal】 p+r AND ITS APPLICATIONS	2001	Takayuki Furuta
+	The Hölder-McCarthy and the Young Inequalities Are Equivalent for Hilbert Space Operators	2001	Takayuki Furuta
+ PDF Chat	Spectral order A ≻ B if and only if A^(2p-r) ≥ ( A^(-r / 2) B^p A^(-r / 2) )^( (2p-r) / (p-r) ) for all p > r ≥ 0 and its application	2001	Takayuki Furuta
+	The Holder-McCarthy and the Young Inequalities Are Equivalent for Hilbert Space Operators	2001	Takayuki Furuta
+	Logarithmic order and dual logarithmic order	2001	Takayuki Furuta
+	LOGARITHMIC ORDER AND DUAL LOGARITHMIC ORDER (Operator Inequalities and Related Area)	2000	Takayuki Furuta
+	Order Preserving Operator Function via Furuta Inequality “A ≥ B ≥ 0 Ensures for $$ \left( {A^{\frac{r} {2}} A^P A^{\frac{r} {2}} } \right)^{\frac{{1 + r}} {{p + r}}} \geqslant \left( {A^{\frac{r} {2}} B^p A^{\frac{r} {2}} } \right)^{\frac{{1 + r}} {{p + r}}} $$ for p≥1 and r≥0”	2000	Takayuki Furuta Takeaki Yamazaki Masahiro Yanagida
+	On powers of -hyponormal and log-hyponormal operators	2000	Takayuki Furuta Masahiro Yanagida
+ PDF Chat	Results under log A ≥ log B can be derived from ones under A ≥ B ≥ 0 by Uchiyama's method - associated with Furuta and Kantorovich type operator inequalities	2000	Takayuki Furuta
+ PDF Chat	Simple proof of the concavity of operator entropy f(A)= -A log A	2000	Takayuki Furuta
+	APPLICATIONS OF GRAMIAN TRANSFORMATION FORMULA	2000	Masatoshi Fujii Takayuki Furuta Ritsuo Nakamoto
+	On powers of <inline-formula><graphic file="1029-242X-2000-892676-i1.gif"/></inline-formula>-hyponormal and log-hyponormal operators	2000	Takayuki Furuta Yanagida Masahiro
+	A subclass of paranormal including class of log-hyponormal and several related classes (Operator Inequalities and related topics)	1999	Takeaki Yamazaki Masatoshi Ito Takayuki Furuta
+	A ≥ B ≥ 0 Ensures $${\left( {{B^{\frac{r}{2}}}{A^p}{B^{\frac{r}{2}}}} \right)^{\frac{1}{q}}} \geqslant {\left( {{B^{\frac{r}{2}}}{A^p}{B^{\frac{r}{2}}}} \right)^{\frac{1}{q}}}$$ for R ≥ 0, P ≥ 0, G ≥ 1 with (1 + R)Q ≥P + R and its Recent Appications	1999	Takayuki Furuta
+ PDF Chat	Generalized Furuta inequality in Banach ✻-algebras and its applications	1999	Takayuki Furuta
+	On a conjecture related to Furuta-type inequalities with negative powers	1998	Takayuki Furuta Takeaki Yamazaki Masahiro Yanagida
+	ORDER PRESERVING OPERATOR INEQUALITIES VIA FURUTA INEQUALITY	1998	Takayuki Furuta Takeaki Yamazaki Masahiro Yanagida
+	An Operator Version Of The Wilf-Diaz-Metcalf Inequality	1998	Jun Ichi Fujii Takayuki Furuta
+	Order preserving operator function via the inequality (Applied Functional Analysis)	1998	Masahiro Yanagida Takeaki Yamazaki Takayuki Furuta
+	Generalized Means and Convexity of Inversion For Positive Operators	1998	Takayuki Furuta Masahiro Yanagida
+	Generalized Means and Convexity of Inversion for Positive Operators	1998	Takayuki Furuta Masahiro Yanagida
+ PDF Chat	A decreasing operator function associated with the Furuta inequality	1998	Takayuki Furuta Derming Wang
+	Operator inequalities associated with Hölder–McCarthy and Kantorovich inequalities	1998	Takayuki Furuta
+ PDF Chat	Simplified proof of an order preserving operator inequality	1998	Takayuki Furuta
+ PDF Chat	Operator functions implying generalized Furuta inequality	1998	Takayuki Furuta Takeaki Yamazaki Masahiro Yanagida
+	Operator inequalities associated with Hölder–McCarthy and Kantorovich inequalities	1998	Takayuki Furuta
+	OPERATOR INEQUALITIES AND COVARIANCE IN NONCOMMUTATIVE PROBABILITY	1997	Masatoshi Fujii Takayuki Furuta Ritsuo Nakamoto Sin-Ei Takahashi
+	Further extensions of aluthge transformation onp-hyponormal operators	1997	Takayuki Furuta Masahiro Yanagida
+	Equivalence relations among reid, L�wner-Heinz and Heinz-Kato inequalities, and extensions of these inequalities	1997	Takayuki Furuta
+	Applications of order preserving operator inequalities to a generalized relative operator entropy	1997	Takayuki Furuta
+ PDF Chat	Extensions of Hölder–McCarthy and Kantorovich inequalities and their applications	1997	Takayuki Furuta
+	Characterizations of chaotic order via generalized Furuta inequality	1997	Takayuki Furuta
+ PDF Chat	Norm inequalities in the Corach-Porta-Recht theory and operator means	1996	Masatoshi Fujii Takayuki Furuta Ritsuo Nakamoto
+	Generalizations of Kosaki trace inequalities and related trace inequalities on chaotic order	1996	Takayuki Furuta
+ PDF Chat	Generalized Aluthge transformation on 𝑝-hyponormal operators	1996	Takayuki Furuta
+	Extension of the furuta inequality and Ando-Hiai log-majorization	1995	Takayuki Furuta
+	A note on the arithmetic-geometric mean inequality for every unitarily invariant matrix norm	1994	Takayuki Furuta
+	$A \ge B \ge 0$ ensures $(B^r A^p B^r)^{1/q} \ge (B^r B^p B^r)^{1/q}$ for $r \ge 0, p \ge 0, q \ge 1$ with (1 + 2r)q $\ge$ p + 2r and its applications(Linear Operators and Inequalities)	1994	Takayuki Furuta
+ PDF Chat	An Extension of the Heinz-Kato Theorem	1994	Takayuki Furuta
+ PDF Chat	An extension of the Heinz-Kato theorem	1994	Takayuki Furuta
+ PDF Chat	Determinant type generalizations of Heinz-Kato theorem via Furuta inequality	1994	Takayuki Furuta
+	Determinant Type Generalizations of the Heinz-Kato Theorem Via the Furuta Inequality	1994	Takayuki Furuta
+ PDF Chat	Complements to the Furuta inequality	1994	Masatoshi Fujii Takayuki Furuta Eizaburo Kamei
+	An Inequality for some Nonnormal Operators--Extension to Normal Approximate Eigenvalues	1993	Masatoshi Fujii Takayuki Furuta Yuki Seo
+ PDF Chat	Norm Inequalities Equivalent to Heinz Inequality	1993	Jun Ichi Fujii Masatoshi Fujii Takayuki Furuta Ritsuo Nakamoto
+ PDF Chat	Norm inequalities equivalent to Heinz inequality	1993	Junichi Fujii Masatoshi Fujii Takayuki Furuta Ritsuo Nakamoto
+	Furuta's inequality and its application to Ando's theorem	1993	Masatoshi Fujii Takayuki Furuta Eizaburo Kamei
+ PDF Chat	An inequality for some nonnormal operators―extension to normal approximate eigenvalues	1993	Masatoshi Fujii Takayuki Furuta Yūki Seo
+	Generalization of Heinz-Kato Theorem Via Furuta Inequality	1993	Takayuki Furuta
+	Applications of the Furuta Inequality to Operator Inequalities and Norm Inequalities Preserving Some Orders	1993	Takayuki Furuta
+	Counterexample to a question on the operator equation T(H1nT)n=K	1992	Edward Bach Takayuki Furuta
+	Applications of Order Preserving Operator Inequalities	1992	Takayuki Furuta
+	Norm inequalities related to Mcintosh type inequality	1992	Jun Ichi Fujii Masatoshi Fujii Takayuki Furuta Ritsuo Nakamoto
+	An Application of Furuta’s Inequality to Ando’s Theorem	1992	Masatoshi Fujii Takayuki Furuta Eizaburo Kamei
+	Operator functions associated with Furuta's inequality	1991	Masatoshi Fujii Takayuki Furuta Eizaburo Kamei
+ PDF Chat	Two Operator Functions with Monotone Property	1991	Takayuki Furuta
+	When Does The Equality Of A Generalized Selberg Inequality Hold	1991	Takayuki Furuta
+ PDF Chat	Two operator functions with monotone property	1991	Takayuki Furuta
+	A proof via operator means of an order preserving inequality	1989	Takayuki Furuta
+ PDF Chat	An elementary proof of an order preserving inequality	1989	Takayuki Furuta
+ PDF Chat	NORM INEQUALITIES EQUIVALENT TO LÖWNER-HEINZ THEOREM	1989	Takayuki Furuta
+	A ≧B ≧0 Ensures (BA 2 B) 1/2 ≧B 2 -Solution to a Conjecture on Operator Inequalities	1988	Takayuki Furuta
+	<i>A</i> ≧ <i>B</i> ≧ 0 Ensures (<i>BA</i><sup>2</sup>)<i>B</i><sup>1/2</sup> ≧ B<sup>2</sup> — Solution to a Conjecture on Operator Inequalities	1988	Takayuki Furuta
+ PDF Chat	An Inequality for Some Nonnormal Operators	1988	Takayuki Furuta
+	The operator equation T(H1nT)n=K	1988	Takayuki Furuta
+ PDF Chat	Two Mixed Hadamard Type Generalizations of Heinz Inequality	1988	Takayuki Furuta
+ PDF Chat	Two mixed Hadamard type generalizations of Heinz inequality	1988	Takayuki Furuta
+ PDF Chat	An inequality for some nonnormal operators	1988	Takayuki Furuta
+	$A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$	1987	Takayuki Furuta
+	A Counterexample to a Conjectured Hermitian Matrix Inequality	1987	Takayuki Furuta
+	A Counterexample to a Conjectured Hermitian Matrix Inequality	1987	Takayuki Furuta
+ PDF Chat	𝐴≥𝐵≥0 assures (𝐵^{𝑟}𝐴^{𝑝}𝐵^{𝑟})^{1/𝑞}≥𝐵^{(𝑝+2𝑟)/𝑞} for 𝑟≥0, 𝑝≥0, 𝑞≥1 with (1+2𝑟)𝑞≥𝑝+2𝑟	1987	Takayuki Furuta
+	A ≥ B ≥ 0 assures (BrApBr)1/q≥ B(P+2r)/qFOR r ≥ 0, p≥0, q≥1 with (1 + 2r)q ≥ p + 2r	1987	Takayuki Furuta
+	Shorter Notes: A Simplified Proof of Heinz Inequality and Scrutiny of its Equality	1986	Takayuki Furuta
+ PDF Chat	Similarity between Kleinecke-Shirokov theorem and Fuglede-Putnam theorem	1986	Takayuki Furuta
+ PDF Chat	A simplified proof of Heinz inequality and scrutiny of its equality	1986	Takayuki Furuta
+ PDF Chat	Mixed Hadamard’s theorems	1986	Takayuki Furuta
+ PDF Chat	Extensions of the Fuglede-Putnam-type theorems to subnormal operators	1985	Takayuki Furuta
+	A COUNTER EXAMPLE TO A RESULT ON APPROXIMATE POINT SPECTRA OF POLAR FACTORS OF HYPONORMAL OPERATORS	1984	Takayuki Furuta
+ PDF Chat	A Hilbert-Schmidt norm inequality associated with the Fuglede-Putnam theorem	1982	Takayuki Furuta
+ PDF Chat	A Hilbert-Schmidt norm inequality associated with the Fuglede-Putnam theorem	1982	Takayuki Furuta
+ PDF Chat	Generalized Fuglede-Putnam theorem and Hilbert-Schmidt norm inequality	1982	Takayuki Furuta
+ PDF Chat	Necessary and sufficient conditions for spectral sets	1981	Takayuki Furuta Muneo Chō
+ PDF Chat	Essentially Convexoid Operators	1981	Takayuki Furuta
+ PDF Chat	An Extension of the Fuglede-Putnam Theorem to Subnormal Operators Using a Hilbert-Schmidt Norm Inequality	1981	Takayuki Furuta
+ PDF Chat	An extension of the Fuglede-Putnam theorem to subnormal operators using a Hilbert-Schmidt norm inequality	1981	Takayuki Furuta
+	Normality can be Relaxed in the Asymptotic Fuglede-Putnum Theorem	1980	Takayuki Furuta
+ PDF Chat	Normality can be relaxed in the asymptotic Fuglede-Putnam theorem	1980	Takayuki Furuta
+ PDF Chat	On Relaxation of Normality in the Fuglede-Putnam Theorem	1979	Takayuki Furuta
+ PDF Chat	On relaxation of normality in the Fuglede-Putnam theorem	1979	Takayuki Furuta
+ PDF Chat	Relations Between Generalized Growth Conditions and Several Classes of Convexoid Operators	1977	Takayuki Furuta
+ PDF Chat	On partial isometries	1977	Takayuki Furuta
+	An application of unitary ϱ-dilations of Sz.-Nagy and Foiaş	1972	Takayuki Furuta
+ PDF Chat	Certain Numerical Radius Contraction Operators	1971	Takayuki Furuta Ritsuo Nakamoto
+ PDF Chat	On the numerical range of an operator	1971	Takayuki Furuta Ritsuo Nakamoto
+ PDF Chat	Certain convexoid operators	1971	Takayuki Furuta
+ PDF Chat	Certain numerical radius contraction operators	1971	Takayuki Furuta Ritsuo Nakamoto
+ PDF Chat	On some theorems of Berberian and Sheth	1970	Takayuki Furuta Ritsuo Nakamoto
+ PDF Chat	A note on two inequalities correlated to unitary $\rho $-dilatations	1969	Takayuki Furuta
+ PDF Chat	Some theorems on certain contraction operators	1969	Takayuki Furuta Ritsuo Nakamoto
+	Some Theorems on Certain Contraction Operators	1969	Takayuki Furuta Ritsuo Nakamoto
+ PDF Chat	A metric characterization of the Cartesean decomposition in a $*$-algebra	1968	Takayuki Furuta Ritsuo Nakamoto
+ PDF Chat	Relations between unitary $\rho$-dilatations and two norms	1968	Takayuki Furuta
+ PDF Chat	Relations between unitary $\rho$-dilatations and two norms, II	1968	Takayuki Furuta
+ PDF Chat	A characterization of spectraloid operators and its generalization	1967	Takayuki Furuta Zirô Takeda
+ PDF Chat	A generalization of Durszt's theorem on unitary $\rho $-dilatations	1967	Takayuki Furuta
+ PDF Chat	On the class of paranormal operators	1967	Takayuki Furuta
+	A Generalization of Durszt's Theorem on Unitary ρ-Dilatations	1967	Takayuki Furuta

Common Coauthors

Coauthor	Papers Together
Ritsuo Nakamoto	13
Masahiro Yanagida	12
Masatoshi Fujii	10
Takeaki Yamazaki	8
Eizaburo Kamei	5
Jun Ichi Fujii	3
Mariko Giga	3
Masatoshi Ito	2
Masatoshi Fujii	2
Josip ‎Pečarić	2
Yūki Seo	2
Derming Wang	1
Masatoshi Ito	1
Yanagida Masahiro	1
Junichi Fujii	1
Lambert Alan	1
Edward Bach	1
Muneo Chō	1
Zirô Takeda	1
Jadranka Mičić	1
Sin-Ei Takahashi	1
Yuki Seo	1
Jung Il Bong	1

Commonly Cited References

Action	Title	Year	Authors	# of times referenced
+ PDF Chat	An elementary proof of an order preserving inequality	1989	Takayuki Furuta	31
+ PDF Chat	Best possibility of the Furuta inequality	1996	Kôtarô Tanahashi	28
+	Beiträge zur Störungstheorie der Spektralzerleung	1951	Erhard Heinz	27
+	Extension of the furuta inequality and Ando-Hiai log-majorization	1995	Takayuki Furuta	26
+	Log majorization and complementary Golden-Thompson type inequalities	1994	Tsuyoshi Andô Fumio Hiai	22
+ PDF Chat	Some operator monotone functions	1972	Gert K. Pedersen	22
+ PDF Chat	Mean theoretic approach to the grand Furuta inequality	1996	Masatoshi Fujii Eizaburo Kamei	18
+	Means of positive linear operators	1980	Fumio Kubo Tsuyoshi Andô	17
+	A proof via operator means of an order preserving inequality	1989	Takayuki Furuta	17
+ PDF Chat	The best possibility of the grand Furuta inequality	1999	Kôtarô Tanahashi	15
+	Invitation to Linear Operators	2001	Takayuki Furuta	15
+	Applications of Order Preserving Operator Inequalities	1992	Takayuki Furuta	15
+	On some operator inequalities	1987	T. Andô	15
+ PDF Chat	Two operator functions with monotone property	1991	Takayuki Furuta	13
+ PDF Chat	Simplified proof of Tanahashi's result on the best possibility of generalized Furuta inequality	1999	Takeaki Yamazaki	13
+	A short proof of the best possibility for the grand Furuta inequality	1999	Masatoshi Fujii Akemi Matsumoto Ritsuo Nakamoto	13
+ PDF Chat	Simplified proof of an order preserving operator inequality	1998	Takayuki Furuta	12
+ PDF Chat	A note on the entropy for operator algebras	1961	Masahiro Nakamura Hisaharu Umegaki	12
+ PDF Chat	A Hilbert Space Problem Book	1982	Paul R. Halmos	12
+	Furuta's inequality and its application to Ando's theorem	1993	Masatoshi Fujii Takayuki Furuta Eizaburo Kamei	10
+	A HILBERT SPACE PROBLEM BOOK	1968	Frank Smithies	10
+	Positive Definite Matrices	2009	Rajendra Bhatia	9
+	$A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$	1987	Takayuki Furuta	9
+	Operator functions associated with Furuta's inequality	1991	Masatoshi Fujii Takayuki Furuta Eizaburo Kamei	9
+	On Normal Operators in Hilbert Space	1951	C. R. Putnam	8
+	Notes on some inequalities for linear operators	1952	Tosio Kato	8
+	Some results on matrix monotone functions	1989	Man Kam Kwong	7
+ PDF Chat	Note on a theorem of Fuglede and Putnam	1959	S. K. Berberian	7
+ PDF Chat	Some exponential operator inequalities	1999	Mitsuru Uchiyama	7
+ PDF Chat	On the class of paranormal operators	1967	Takayuki Furuta	6
+ PDF Chat	Note on a Theorem of Fuglede and Putnam	1959	S. K. Berberian	6
+	Shorter Notes: Some Operator Monotone Functions	1972	Gert K. Pedersen	6
+	A matrix version of the Ky Fan generalization of the kantorovich inequality	1994	B. Mond Jozep Pecaric	6
+	A characterization of chaotic order and a problem	1998	Masatoshi Fujii Jian Fei Jiang Eizaburo Kamei Kôtarô Tanahashi	6
+ PDF Chat	Results under log A ≥ log B can be derived from ones under A ≥ B ≥ 0 by Uchiyama's method - associated with Furuta and Kantorovich type operator inequalities	2000	Takayuki Furuta	6
+	Onp-hyponormal operators for 0<p<1	1990	Ariyadasa Aluthge	6
+ PDF Chat	Operator functions implying generalized Furuta inequality	1998	Takayuki Furuta Takeaki Yamazaki Masahiro Yanagida	6
+ PDF Chat	On relaxation of normality in the Fuglede-Putnam theorem	1979	Takayuki Furuta	5
+ PDF Chat	A note on $p$-hyponormal operators	1997	Tadasi Huruya	5
+	Operator inequalities associated with Hölder–McCarthy and Kantorovich inequalities	1998	Takayuki Furuta	5
+	The Golden-Thompson trace inequality is complemented	1993	Fumio Hiai Dėnes Petz	5
+ PDF Chat	Extensions of a theorem of Fuglede and Putnam	1978	S. K. Berberian	5
+ PDF Chat	Extensions of a Theorem of Fuglede and Putnam	1978	S. K. Berberian	5
+	An operator inequality	1980	Frank Hansen	5
+	On a Theorem of Fuglede and Putnam<sup>†</sup>	1958	Marvin Rosenblum	5
+ PDF Chat	𝐴≥𝐵≥0 assures (𝐵^{𝑟}𝐴^{𝑝}𝐵^{𝑟})^{1/𝑞}≥𝐵^{(𝑝+2𝑟)/𝑞} for 𝑟≥0, 𝑝≥0, 𝑞≥1 with (1+2𝑟)𝑞≥𝑝+2𝑟	1987	Takayuki Furuta	5
+	Hermitian Matrix Inequalities and a Conjecture	1985	N. N. Chan Man Kam Kwong	5
+	Shifts on Hilbert spaces.	1961	Paul R. Halmos	5
+ PDF Chat	Characterization of chaotic order and its application to Furuta inequality	1997	Masatoshi Fujii Jian Fei Jiang Eizaburo Kamei	4
+ PDF Chat	A decreasing operator function associated with the Furuta inequality	1998	Takayuki Furuta Derming Wang	4