Additive results for the generalized Drazin inverse in a Banach algebra. (English) Zbl 1104.47040

Summary: There are investigated additive properties of the generalized Drazin inverse in a Banach algebra. The authors give some new conditions under which the generalized Drazin inverse of the sum \(a + b\) could be explicitly expressed in terms of \(a\), \(b\) and their generalized Drazin inverse \(a^{d}\), \(b^{d}\). Also, some recent results of N. Castro González and J. J. Koliha [Proc. R. Soc. Edinb., Sect. A, Math. 134, No. 6, 1085–1097 (2004; Zbl 1088.15006)] are extended.


47C05 Linear operators in algebras
15A09 Theory of matrix inversion and generalized inverses
46H30 Functional calculus in topological algebras
46H05 General theory of topological algebras


Zbl 1088.15006
Full Text: DOI


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