Operator Aczel inequality

TL;DR

This paper develops multiple operator versions of the classical Aczel inequality, extending it to contexts involving weighted operator geometric means and positive sesquilinear forms, with applications to $C^*$-algebras and matrix norms.

Contribution

It introduces new operator inequalities related to Aczel's inequality, incorporating weighted geometric means and sesquilinear forms, with practical applications in $C^*$-algebra maps and matrix norms.

Findings

Established operator inequalities involving weighted geometric means.

Extended Aczel inequality to positive sesquilinear forms.

Applied results to unital positive linear maps and unitarily invariant norms.

Abstract

We establish several operator versions of the classical Aczel inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the unital positive linear maps on $C^*$-algebras and the unitarily invariant norms on matrices are presented.