Extensions of the pseudo Drazin inverse in Banach algebras

Abstract

In this paper, we study a new class of generalized inverse in Banachalgebras, which is termed extended pseudo Drazin inverse. We derive several characterizations and elementary properties of the extended pseudo Drazin inverse. Moreover, we obtain the generalized versions of Jacobson’s lemma for extended Drazin inverse, extended generalized Drazin inverse and extended pseudo Drazin inverse.