TWO TRACE INEQUALITIES FOR OPERATOR FUNCTIONS

摘要

In this paper we show that for a non-negative operator monotone function f on [0,infinity) such that f (0) = 0 and for any positive semidefinite matrices A and B, Tr((A - B)(f (A) - f (B))) <= Tr(vertical bar A - B vertical bar f (vertical bar A - B vertical bar)). When the function f is operator convex on [0,infinity), the inequality is reversed.