Some inequalities for the Euclidean operator radius of two operators in Hilbert $C^{\ast}$-Modules space

TL;DR

This paper establishes new bounds for the Euclidean operator radius of two operators in Hilbert C*-modules and relates these bounds to existing results on the numerical radius of linear operators.

Contribution

It provides novel inequalities for the Euclidean operator radius in Hilbert C*-modules, extending and connecting to recent bounds on the numerical radius.

Findings

Derived precise bounds for the Euclidean operator radius.

Connected the bounds to recent numerical radius inequalities.

Enhanced understanding of operator behavior in Hilbert C*-modules.

Abstract

The Euclidean operator radius of two bounded linear operators in the Hilbert $C^*$-module over $\A$ is given some precise bounds. Their relationship to recent findings in the literature that offer precise upper and lower bounds on the numerical radius of linear operators is also established.