A convex treatment of numerical radius inequalities

TL;DR

This paper introduces a convex approach to derive new numerical radius inequalities for Hilbert space operators, extending existing results and defining a generalized numerical radius.

Contribution

It presents a novel convex function-based method for numerical radius inequalities, offering generalized and extended forms beyond previous approaches.

Findings

New numerical radius inequalities derived

Generalized numerical radius introduced

Extensions of classical results achieved

Abstract

In this article, we prove an inner product inequality for Hilbert space operators. This inequality, then, is utilized to present a general numerical radius inequality using convex functions. Applications of the new results include obtaining new forms that generalize and extend some well known results in the literature, with an application to the newly defined generalized numerical radius. We emphasize that the approach followed in this article is different from the approaches used in the literature to obtain the refined versions.