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The weighted g-Drazin inverse for operators

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

References

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