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On Some Trace Inequalities


Trung Hoa Dinh, Raluca Dumitru, Jose A. Franco, Cong Trinh Le*

Source title: 
Mathematical Inequalities and Applications, 23(2): 467-476, 2020 (ISI)
Academic year of acceptance: 

In this paper we consider some generalizations of Ando's 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 non-negative functions function f on [0, ∞) 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.