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The weighted g-Drazin inverse for operators

Part of: Topological algebras, normed rings and algebras, Banach algebras General theory of linear operators

Published online by Cambridge University Press:  09 April 2009

A. Dajić  and
J. J. Koliha
J. J. Koliha
Affiliation:
Department of Mathematics and Statistics The University of MelbourneVIC 3010Australia e-mail: a.dajic@ms.unimelb.edu.au, j.koliha@ms.unimelb.edu.au
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Abstract

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The paper introduces and studies the weighted g-Drazin inverse for bounded linear operators between Banach spaces, extending the concept of the weighted Drazin inverse of Rakočević and Wei (Linear Algebra Appl. 350 (2002), 25–39) and of Cline and Greville (Linear Algebra Appl. 29 (1980), 53–62). We use the Mbekhta decomposition to study the structure of an operator possessing the weighted g-Drazin inverse, give an operator matrix representation for the inverse, and study its continuity. An open problem of Rakočević and Wei is solved.

Keywords

Banach algebra without unitg-Drazin inversebounded linear operatorweighted g-Drazin inversethe Mbekhta decompositionascent and descent.

MSC classification

Secondary: 47A60: Functional calculus 46H30: Functional calculus in topological algebras 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 47A10: Spectrum, resolvent
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 2 , April 2007 , pp. 163 - 181
Copyright
Copyright © Australian Mathematical Society 2007

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