An extension of the $\rho$-operator radii

TL;DR

This paper introduces a new function on the algebra of bounded linear operators that generalizes existing operator radii, extending several known results in the field.

Contribution

It defines a novel operator function on $C^{ ext{*}}$-algebras that broadens the scope of operator radii and generalizes prior theoretical results.

Findings

Established basic properties of the new operator function

Extended several classical results in operator theory

Provided a framework for future generalizations

Abstract

We define a function on the $C^{\ast}$-algebra of all bounded linear Hilbert space operators, which generalizes the operator radii, and we present some basic properties of this function. Our results extend several results in the literature.