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Two Trace Inequalities For Operator Functions

Authors: 

Trung Hoa Dinh, Minh Toan Ho, Cong Trinh Le*, Bich Khue Vo

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((− B)(f(A) − f(B)))  Tr(|− B| f(|− B|)).
When the function f is operator convex on [0,∞), the inequality is reversed.