Inequalities for positive linear maps on Hermitian matrices
Jadranka Mić ć Hot, Josip E. Pečarić, Yūki Seo, Masaru Tominaga · Mathematical Inequalities & Applications · 2000
The aim of this work is to generalize the main inequalities in [9] as follows: Let A be a Hermitian matrix, let be a normalized positive linear map, let f and g be real valued continuous functions and let F(u, v) be a real valued function matrix non-decreasing in its first variable. Real constants and such that I F [ (f (A)) , g ((A))] I are determined. If f is a concave (resp. convex) function then the determination of (resp. ) is reduced to solving a single variable maximization (resp. minimization) problem. Some applications of these results to the power function, the means and the Hadamard product are also given.