New estimates for numerical radius in $C^*$-algebras

TL;DR

This paper extends numerical radius inequalities within $C^*$-algebras using a generalized Buzano inequality, providing broader bounds and insights into operator theory.

Contribution

It introduces new numerical radius inequalities in $C^*$-algebras based on an extended Buzano inequality, generalizing previous results.

Findings

New inequalities for numerical radius in $C^*$-algebras

Extension of Buzano inequality to pre-Hilbert $C^*$-modules

Generalization of earlier numerical radius bounds

Abstract

Several numerical radius inequalities in the framework of $C^*$-algebras are proved in this paper. These results, which are based on an extension of Buzano inequality for elements in a pre-Hilbert $C^*$-module, generalize earlier numerical radius inequalities.