On a new norm on $\mathcal{B}({\mathcal{H}})$ and its applications to numerical radius inequalities

TL;DR

This paper introduces a new operator norm on Hilbert space operators that generalizes existing norms and provides improved bounds for numerical radius inequalities, enhancing understanding of operator behavior.

Contribution

The paper proposes a novel norm on bounded operators that unifies and extends the numerical radius, operator norm, and Davis-Wielandt radius, with applications to tighter bounds.

Findings

Derived bounds for the new norm's upper and lower limits.

Improved numerical radius inequalities compared to existing results.

Examples demonstrating the effectiveness of the new bounds.

Abstract

We introduce a new norm on the space of bounded linear operators on a complex Hilbert space, which generalizes the numerical radius norm, the usual operator norm and the modified Davis-Wielandt radius. We study basic properties of this norm, including the upper and the lower bounds for it. As an application of the present study, we estimate bounds for the numerical radius of bounded linear operators. We illustrate with examples that our results improve on some of the important existing numerical radius inequalities.