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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.

MSC:

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

Citations:

Zbl 1088.15006
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References:

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