Representations for the Generalized Drazin Inverse of the Sum in a Banach Algebra and Its Application for Some Operator Matrices

Abstract

We investigate additive properties of the generalized Drazin inverse in a Banach algebra A. We find explicit expressions for the generalized Drazin inverse of the sum a+b, under new conditions on a,b∈A. As an application we give some new representations for the generalized Drazin inverse of an operator matrix.