Results 81 to 90 of about 1,171 (115)

More accurate classes of Jensen-type inequalities for convex and operator convex functions

, 2018
Motivated by a recent refinement of the scalar Jensen inequality obtained via linear interpolation, in this paper we develop a general method for improving two classes of Jensen-type inequalities for bounded self-adjoint operators. The first class refers
D. Choi, M. Krnić, J. Pečarić
semanticscholar   +1 more source

Precise estimates of bounds on relative operator entropies [PDF]

arXiv, 2014
Recently, Zou obtained the generalized results on the bounds for Tsallis relative operator entropy. In this short paper, we give precise bounds for Tsallis relative operator entropy. We also give precise bounds of relative operator entropy.
arxiv  

Eigenvalue inequalities related to the Ando-Hiai inequality

, 2017
In this paper, we show that if f is a doubly concave function on [0,∞) and 0 < sA B tA for some scalars 0 < s t with w = t/s , then for every k = 1,2, · · · ,n , λk( f (A) f (B)) w 1 4 +w− 1 4 2 λk( f (A B)), where A B = A 1 2 (A− 1 2 BA− 1 2 ) 1 2 A 1 2
M. Ghaemi, V. Kaleibary
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Noncommutative Perspectives of Operator Monotone Functions in Hilbert Spaces [PDF]

arXiv, 2020
Some identities for noncommutative perspectives of operator monotone functions in Hilbert spaces aregiven. Applications for weighted operator geometric mean and relative operator entropy are also provided.
arxiv  

Reverses of Ando's inequality for positive linear maps

, 2011
Ando’s inequality says that if A and B are positive operators on a Hilbert space H and Φ is a positive linear map, then for each α ∈ [0,1] Φ(A α B) Φ(A) α Φ(B) where the α -geometric mean is defined by A α B = A 1 2 ( A− 1 2 BA− 1 2 )α A 1 2 .
Y. Seo
semanticscholar   +1 more source

Quadratic Weighted Geometric Mean in Hermitian Unital Banach Star-Algebras [PDF]

arXiv, 2016
In this paper we introduce the quadratic weighted geometric mean for invertible elements x, y in a Hermitian unital Banach star-algebra and provide some inequalities for this mean under various assumptions for the elements involved.
arxiv  

On Some Numerical Radius Inequalities for Hilbert Space Operators [PDF]

arXiv, 2020
This article is devoted to studying some new numerical radius inequalities for Hilbert space operators. Our analysis enables us to improve an earlier bound of numerical radius due to Kittaneh.
arxiv  

Heinz-Kato inequality in Banach spaces [PDF]

J. Anal. 28, no. 3, 841-846 (2020), 2018
It is observed that in Banach spaces, sectorial operators having bounded imaginary powers satisfy a Heinz-Kato inequality.
arxiv  

An Operator Inequality Which Implies Paranormality

, 1999
Let T be a bounded linear operator on a Hilbert space. Among other things, it is shown that (1) if |T2| |T|2 , then T is paranormal, (2) if T is w -hyponormal, then |T2| |T|2 and |T∗ | |T∗|2 , and (3) if T and T∗ are w -hyponormal, and either ker T ⊆ ker
Ariyadasa Aluthge, Derming Wang
semanticscholar   +1 more source

Numerical radius inequalities associated with the Cartesian decomposition

, 2015
We give several sharp numerical radius inequalities associated with the Cartesian decomposition of a Hilbert space operator A = B + iC . Among other inequalities, it is shown that 1 2 ‖ |B| + |C|‖ wr(A) ‖ |B| + |C|‖ for 0 < r 2 , where w(·) and ...
F. Kittaneh
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