On generalized Powers-St$\o$rmer's Inequality

TL;DR

This paper extends Powers-Størmer's inequality to a broader class of operator monotone functions and positive linear functionals on $C^*$-algebras, providing a characterization of tracial functionals.

Contribution

It introduces a generalized form of Powers-Størmer's inequality applicable to operator monotone functions and positive linear functionals on $C^*$-algebras, and characterizes tracial functionals.

Findings

Generalized Powers-Størmer's inequality proved.

Characterization of tracial functionals on $C^*$-algebras.

Applicable to operator monotone functions on $[0, + abla$]

Abstract

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