Additive Results of the Drazin Inverse for Bounded Linear Operators

摘要

Given two bounded linear operators P and Q on aBanach space the formula for the Drazin inverse of P + Q is given, under the assumptions P~2Q + PQ~2 = 0 and P~3Q = 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.