Upper bounds of numerical radius and $a$-numerical radius in $\mathcal{C}^*$-algebra setting using Orlicz functions

TL;DR

This paper establishes new upper bounds for the numerical radius and $a$-numerical radius in $ ext{C}^*$-algebras using Orlicz functions, unifying and extending existing results.

Contribution

It introduces a novel approach to bounding numerical radii in $ ext{C}^*$-algebras via Orlicz functions, generalizing many known inequalities.

Findings

Derived new upper bounds for numerical radius

Extended bounds to $a$-numerical radius

Unified existing results through Orlicz functions

Abstract

In this paper, several significant upper bounds for the numerical radius and $a$-numerical radius of an element in a $\mathcal{C}^*$-algebra are obtained using Orlicz functions. Many well-known results are obtained from our findings, depending on specific choices of Orlicz functions.