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Additive results for the generalized Drazin inverse

Part of: Basic linear algebra General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

Dragan S. Djordjević  and
Yimin Wei
Dragan S. Djordjević
Affiliation:
Department of Mathematics, Faculty of Sciences, University of Niš, P.O. Box 224, 18000 Niš, Yugoslavia e-mail: [email protected]
Yimin Wei
Affiliation:
Department of Mathematics, and Laboratory of Mathematics, for Nonlinear Sciences, Fudan University, Shanghai 200433, P.R. of China e-mail: [email protected]
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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.

Keywords

generalized Drazin inverseperturbationsadditive results

MSC classification

Secondary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A55: Perturbation theory 15A09: Matrix inversion, generalized inverses
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 1 , August 2002 , pp. 115 - 126
Copyright
Copyright © Australian Mathematical Society 2002

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