Generalized A-numerical radius inequalities in semi-Hilbert spaces through the angle between two vectors

Abstract

This paper presents several inequalities related to the A-numerical radius in the context of semi-Hilbert space operators. By integrating modern techniques from operator theory and functional analysis, we derive new inequalities for the A-numerical radius that emphasize the unique characteristics of semi-Hilbert space operators. Among other results, it is shown that, if , where A is a positive and onto operator, and T has a polar decomposition given by T = U|T|, and , then