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

摘要

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