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Additive Results of the Drazin Inverse for Bounded Linear Operators
Authors:Junjie Huang  Yunfeng Shi  Alatancang Chen
Institution:1. School of Mathematical Sciences, Inner Mongolia University, Hohhot, 010021, Inner Mongolia, People’s Republic of China
Abstract:Given two bounded linear operators $P$ and $Q$ on a Banach space the formula for the Drazin inverse of $P+Q$ is given, under the assumptions $P^2 Q+PQ^2=0$ and $P^3 Q=PQ^3=0$ . In particular, some recent results arising in Drazin (Am Math Mon 65:506–514, 1958), Hartwig et al. (Linear Algebra Appl 322:207–217, 2001) and Castro-González et al. (J Math Anal Appl 350:207–215, 2009) are extended.
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