Numerical radius inequalities for Hilbert Space Operators

TL;DR

This paper improves existing inequalities related to the numerical radius of Hilbert space operators, providing new bounds and refinements that enhance previous results in the literature.

Contribution

It introduces improved inequalities for the numerical radius of Hilbert space operators, refining and extending earlier known results.

Findings

New inequalities for the numerical radius are established.

Refinements of existing inequalities are demonstrated.

Some results outperform previous literature results.

Abstract

In this work, an improvement of H\"{o}lder-McCarty inequality is established. Based on that, several refinements of the generalized mixed Schwarz inequality are obtained. Consequently, some new numerical radius inequalities are proved. New inequalities for numerical radius of $n\times n$ matrix of Hilbert space operators are proved as well. Some refinements of some earlier results were proved in literature are also given. Some of the presented results are refined and it shown to be better than earlier results were proved in literature.