Title

On some trace inequalities

Document Type

Article

Publication Date

4-1-2020

Subject Area

ARRAY(0x557a95de7778)

Abstract

In this paper we consider some generalizations of the Ando inequality ||| f (A)- f (B)||| ≤ ||| f (|A-B|)||| with the "weight" (A-B)p. More precisely, for p ≥ 1 such that (-1)p= -1 and for a nonnegative function f on [0,8) such that f (0) = 0, we study the following inequality: Tr((A-B)p( f (A)- f (B)))≥ Tr(|A-B|pf (|A-B|)), whenever A and B are positive semidefinite matrices. We show that the inequality is true for any operator convex function f and it is reversed whenever f is operator monotone.

Publication Title

Mathematical Inequalities and Applications

Volume

23

Issue

2

First Page

467

Last Page

476

Digital Object Identifier (DOI)

10.7153/mia-2020-23-38

ISSN

13314343

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