On Some Trace Inequalities
On Some Trace Inequalities
Source title:
Mathematical Inequalities and Applications, 23(2): 467-476,
2020
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
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.