New additive results for the g-Drazin inverse

Author: Castro González N.J.   Koliha J.J.  

Publisher: Royal Society of Edinburgh

ISSN: 1473-7124

Source: Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.134, Iss.6, 2004-12, pp. : 1085-1097

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Abstract

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.