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The Drazin inverse of the sum of two products
Safae Alaoui Chrifi,Abdelaziz Tajmouati 대한수학회 2022 대한수학회논문집 Vol.37 No.3
In this paper, for bounded linear operators $A,B,C$ satisfying $[AB,B]=[BC,B]=[AB,BC]=0$ we study the Drazin invertibility of the sum of products formed by the three operators $A,B$ and $C$. In particular, we give an explicit representation of the anti-commutator $\{A,B\}=AB+BA$. Also we give some conditions for which the sum $A+C$ is Drazin invertible.