Drazin invertibility of sum and product of closed linear operators
Bekkai Messirdi, Sanaa Messirdi, Miloud Messirdi · Malaya Journal of Matematik · 2014
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 $A^D$ are given, we obtain also a useful caracterization and explicit formula for the Drazin inverse $(A+B)^D$ and $(A B)^D$ if $A$ and $B$ are closed operators.