J. Austral. Math. Soc.  73 (2002), 115-125
Additive results for the generalized Drazin inverse

Dragan S. Djordjevic
  Department of Mathematics
  Faculty of Sciences
  University of Nis
  P.O. Box 224
  18000 Nis
Yimin Wei
  Department of Mathematics
  and Laboratory of Mathematics
  for Nonlinear Sciences
  Fudan University
  Shanghai 200433
  P.R. of China

Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, if $A^d$ denotes the generalized Drazin inverse of a bounded linear operator $A$ on an arbitrary complex Banach space, then in some special cases $(A+B)^d$ is computed in terms of $A^d$ and $B^d$. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl. 322 (2001), 207-217) are extended to infinite dimensional settings with simplified proofs.
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