$A$-approximate point spectrum of $A$-bounded operators in semi-Hilbertian spaces

Abstract

This paper delves into several characterizations of $A$-approximate point spectrum of A-bounded operators acting on a complex semi-Hilbertian space $H$ and also investigates properties of the $A$-approximate point spectrum for the tensor product of two $A^{\frac{1}{2}}$-adjoint operators. Furthermore, several properties of $A$-normal operators have been established.