On the numerical range and the numerical radius of operators in C*-algebras

Abstract

The main objective of this paper is to study the properties of the numerical range and numerical radius in C*-algebras. We begin by exploring the relationship between these concepts and the analytic structure of the algebra, establishing several fundamental inequalities and presenting a refinement of the triangle inequality for the numerical radius. Through this study, we specifically aim to generalize and deepen the mathematical understanding of numerical range and numerical radius properties, while developing new analytical tools applicable in various areas of functional analysis and operator theory.