Weighted generalized core-EP inverse in Banach *-algebras

Abstract

In this paper, we introduce the notion of weighted generalized core-EP inverse in a Banach *-algebra. Some properties of weighted core-EP inverse for rectangular complex matrices and bounded linear Hilbert space operators are generalized and some new ones are established. Properties of weighted generalized core-EP orders are presented for all weighted g-Drazin invertible elements in a Banach *-algebra.