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Additive results for the generalized Drazin inverse

Published online by Cambridge University Press:  09 April 2009

Dragan S. Djordjević
Affiliation:
Department of Mathematics, Faculty of Sciences, University of Niš, P.O. Box 224, 18000 Niš, Yugoslavia e-mail: dragan@pmf.pmf.ni.ac.yu
Yimin Wei
Affiliation:
Department of Mathematics, and Laboratory of Mathematics, for Nonlinear Sciences, Fudan University, Shanghai 200433, P.R. of China e-mail: ymwei@fudan.edu.cn
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Abstract

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Additive perturbation results for the generalized Drazin inverse of Banach space operators are presented. Precisely, if Ad 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 Ad and Bd. Thus, recent results of Hartwig, Wang and Wei (Linear Algebra Appl. 322 (2001), 207–217) are extended to infinite dimensional settings with simplified proofs.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2002

References

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