Two Trace Inequalities For Operator Functions
Two Trace Inequalities For Operator Functions
Source title:
Mathematical Inequalities and Applications, 22(3): 1021-1026,
2019
(ISI)
Academic year of acceptance:
2019-2020
Abstract:
In this paper we show that for a non-negative operator monotone function f on [0,∞) such that f(0) = 0 and for any positive semidefinite matrices A and B, Tr((A − B)(f(A) − f(B))) Tr(|A − B| f(|A − B|)).
When the function f is operator convex on [0,∞), the inequality is reversed.