On generalized Powers-St$ø$rmer's Inequality

Abstract

A generalization of Powers-St$ø$rmer's inequality for operator monotone functions on $[0,+\infty )$ and for positive linear functional on general $C^{\ast }$-algebras will be proved. It also will be shown that the generalized Powers-St$ø$rmer inequality characterizes the tracial functionals on $C^{\ast }$-algebras.

This is a revised version which was submitted to LAA