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
  Yugoslavia
  dragan@pmf.pmf.ni.ac.yu
and
Yimin Wei
  Department of Mathematics
  and Laboratory of Mathematics
  for Nonlinear Sciences
  Fudan University
  Shanghai 200433
  P.R. of China
  ymwei@fudan.edu.cn


Abstract
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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