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New additive results for the g-Drazin inverse

Published online by Cambridge University Press:  12 July 2007

N. Castro González
Affiliation:
Facultad de Informática, Universidad Politécnica de Madrid, 28660 Madrid, Spain (nieves@fi.upm.es)
J. J. Koliha
Affiliation:
Department of Mathematics and Statistics, University of Melbourne, VIC 3010, Australia (koliha@unimelb.edu.au)
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Abstract

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This paper studies additive properties of the generalized Drazin inverse (g-Drazin inverse) in a Banach algebra and finds an explicit expression for the g-Drazin inverse of the sum a + b in terms of a and b and their g-Drazin inverses under fairly mild conditions on a and b.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2004