The generalized and pseudo n-strong Drazin inverses in rings

Abstract

We introduce new classes of generalized Drazin inverses in a ring, which are called the generalized n-strong Drazin inverse and pseudo n-strong Drazin inverse for arbitrary . Some basic properties of these inverses are studied. We prove extensions of Cline's formula for these inverses and Jacobson's lemma for generalized and pseudo strong Drazin inverse. In a Banach algebra, we define and characterize the weighted generalized strong Drazin inverse and weighted pseudo strong Drazin inverse.