Drazin invertibility of sum and product of closed linear operators

Abstract

The paper present a survey of results concerning the fundamental properties of the Drazin inverse for bounded operators and an interesting study of the Drazin inverse for a closed operator in a Banach space. Some necessary and sufficient conditions for A closed linear operator to possess a Drazin inverse AD are given, we obtain also a useful caracterization and explicit formula for the Drazin inverse (A+ B) D and (AB) D if A and B are closed operators.