On the Euclidean operator radius and norm

TL;DR

This paper establishes new bounds relating the numerical radius and Euclidean operator norm, introduces the $f$-operator radius, and provides refinements and generalizations of existing results with supporting examples.

Contribution

It presents novel bounds for the numerical radius in terms of the Euclidean operator norm and explores the $f$-operator radius as a generalization, enhancing existing theoretical results.

Findings

New bounds for numerical radius in terms of Euclidean operator norm

Introduction and analysis of the $f$-operator radius

Refinements and generalizations of classical results

Abstract

In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature. Then, the $f$-operator radius, recently defined as a generalization of the Euclidean operator radius, will be studied. Many upper bounds will be found and matched with existing results that treat the numerical radius. Special cases of this discussion will lead to some refinements and generalizations of some well-established results in the field. Further, numerical examples are given to support our findings, and a simple optimization application will be presented.