A Comparison of some Weighted Numerical Radii of Hilbert Space Operators

Abstract

In recent years, several generalizations of the numerical radius for bounded linear operators on Hilbert spaces have been introduced and extensively studied. These generalizations provide refined tools for investigating operator inequalities and spectral properties. In this paper, we investigate several generalized numerical radii and establish relationships among them. We also establish several relationships among these generalized numerical radii and show that the $(s,t)$-weighted numerical radius can be represented as a rescaled form of the $t$-weighted numerical radius.