On some trace inequalities
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.
Mathematical Inequalities and Applications
Digital Object Identifier (DOI)
Dinh, T.H., Dumitru, R., Franco, J.A., Le, C.T. (2020) On some trace inequalities. Mathematical Inequalities and Applications, 23(2), 467-476.