A new seminorm of $n$-tuple operators and its applications

TL;DR

This paper introduces a new seminorm for n-tuple operators that generalizes existing radii, studies its properties, and improves bounds for related numerical radius inequalities in Hilbert space operator theory.

Contribution

It presents a novel seminorm for n-tuple operators, extending the A-Euclidean operator radius, with new bounds and improved inequalities.

Findings

Defined a new seminorm for n-tuple operators.

Derived bounds for the A-Euclidean operator radius.

Enhanced existing A-numerical radius inequalities.

Abstract

We introduce a new seminorm of $n$-tuple operators, which generalizes the $A$-Euclidean operator radius of $n$-tuple bounded linear operators on a complex Hilbert space. We introduce and study basic properties of this seminorm. As an application of the present study, we estimate bounds for the $A$-Euclidean operator radius ($A$-joint numerical radius). In addition, we improve on some of the important existing $A$-numerical radius inequalities and related results.