SOME INEQUALITIES FOR THE WEIGHTED A-NUMERICAL RADIUS

Abstract

In this paper, we propose an alternative formulation of the weighted Anumerical radius ω(A,v)(·) for bounded linear operators on semi-Hilbert spaces induced by a positive operator A. Building upon the framework introduced by Gao and Liu [Oper. Matrices, 17 (2023), 343–354], we derive several new inequalities that offer sharper bounds and refined characterizations of this semi-norm. These results enrich the existing theory by extending the analytical tools available for studying operator behavior in semi-Hilbertian contexts.