Weighted Inequalities For The Numerical Radius

TL;DR

This paper derives new weighted bounds for the numerical radius of operators on Hilbert spaces, generalizing many existing inequalities and providing numerical examples to illustrate the improvements.

Contribution

It introduces generalized weighted inequalities for the numerical radius, extending and refining previous results in the literature.

Findings

New weighted bounds for the numerical radius

Generalizations of existing inequalities

Numerical examples demonstrating refinements

Abstract

In this article, we obtain several new weighted bounds for the numerical radius of a Hilbert space operator. The significance of the obtained results is the way they generalize many existing results in the literature; where certain values of the weights imply some known results, or refinements of these results. In the end, we present some numerical examples that show how our results refine the well known results in the literature, related to this topic.