On generalized core invertibility in Banach algebras

Abstract We introduce a new generalized inverse, called generalized core inverse in a Banach *-algebra. This new inverse is an extension of weak core inverse defined for complex square matrix and bounded linear operators over Hilbert spaces. We present various characterizations of this new inverse. The relationship between the generalized core inverse and other generalized inverses is investigated. Finally, we consider the necessary and sufficient conditions under which generalized core inverse and generalized core-EP inverse coincide with each other in a Banach *-algebra.