Generalized weighted core inverse in Banach *-algebras

Abstract

In this paper, we introduce the notion of the generalized weighted core inverse in a Banach *-algebra. We characterize this new generalized inverse by using the generalized weighted core decomposition and present the representations by the generalized Drazin inverse.
These extend the core-EP inverse and weighted (pseudo) core inverse for complex matrices and linear bounded operators to more general setting.