$q$-Numerical Radius Estimates in Semi-Hilbertian Spaces and Their Relations with Matrix Means for Sectorial Matrices

TL;DR

This paper investigates the $q$-numerical radius in semi-Hilbertian spaces, providing new characterizations, bounds, and inequalities that relate to matrix means and sectorial matrices.

Contribution

It introduces novel characterizations and bounds for the $q$-numerical radius, connecting it with matrix means and operator monotone functions in semi-Hilbertian spaces.

Findings

Established sharp upper and lower bounds for the $q$-numerical radius.

Derived inequalities involving operator monotone functions.

Connected $q$-numerical radius with matrix means for sectorial matrices.

Abstract

In this paper, the $q$-numerical radius of operators in semi-Hilbertian spaces is studied. New characterizations are established, and sharp upper and lower bounds for the $q$-numerical radius are derived. Moreover, several inequalities involving operator monotone functions and matrix means for the $q$-numerical radius of sectorial matrices are obtained.