$A$-numerical radius : New inequalities and characterization of equalities

TL;DR

This paper introduces new bounds for the $A$-numerical radius of semi-Hilbertian space operators, improving existing inequalities and characterizing conditions for equality, thus advancing the theoretical understanding of operator bounds.

Contribution

It develops novel lower bounds for the $A$-numerical radius and characterizes equality cases, enhancing the theoretical framework for semi-Hilbertian space operators.

Findings

New lower bounds for $A$-numerical radius

Improved upper bounds for commutator $A$-numerical radius

Characterizations of equality cases in existing inequalities

Abstract

We develope new lower bounds for the $A$-numerical radius of semi-Hilbertian space operators, and applying these bounds we obtain upper bounds for the $A$-numerical radius of the commutators of operators. The bounds obtained here improve on the existing ones. Further, we provide characterizations for the equality of the existing $A$-numerical radius inequalities of semi-Hilbertian space operators.