Generalized Euclidean Operator Radius

TL;DR

This paper introduces a generalized operator radius for Hilbert space operators, expanding upon existing concepts like the Euclidean and q-operator radii, and explores its properties and implications.

Contribution

It defines the f-operator radius as a new generalization, extending known operator radius results in the literature.

Findings

Properties of the f-operator radius are established.

The new radius generalizes existing operator radii.

Connections to known results are discussed.

Abstract

In this paper, we introduce the $f-$operator radius of Hilbert space operators as a generalization of the Euclidean operator radius and the $q-$operator radius. Properties of the newly defined radius are discussed, emphasizing how it extends some known results in the literature.