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