Cvetković-Ilić, Dragana S.; Djordjević, Dragan S.; Wei, Yimin Additive results for the generalized Drazin inverse in a Banach algebra. (English) Zbl 1104.47040 Linear Algebra Appl. 418, No. 1, 53-61 (2006). 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. Reviewer: D. Przeworska-Rolewicz (Warszawa) Cited in 37 Documents 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 Keywords:Banach algebra; Drazin inverse; generalized Drazin inverse Citations:Zbl 1088.15006 PDF BibTeX XML Cite \textit{D. S. Cvetković-Ilić} et al., Linear Algebra Appl. 418, No. 1, 53--61 (2006; Zbl 1104.47040) Full Text: DOI OpenURL References: [1] Drazin, M.P., Pseudoinverse in associative rings and semigroups, Am. math. month., 65, 506-514, (1958) · Zbl 0083.02901 [2] Koliha, J.J., A generalized Drazin inverse, Glasgow math. J., 38, 367-381, (1996) · Zbl 0897.47002 [3] Harte, R.E., Spectral projections, Irish math. soc. newslett., 11, 10-15, (1984) · Zbl 0556.47001 [4] Harte, R.E., Invertibility and singularity for bounded linear operators, (1988), Marcel Dekker New York · Zbl 0636.47001 [5] Harte, R.E., On quasinilpotents in rings, Panam. math. J., 1, 10-16, (1991) · Zbl 0761.16009 [6] Castro González, N.; Koliha, J.J.; Rakocevic, V., Continuity and general perturbation of the Drazin inverse for closed linear operators, Abstract appl. anal., 7, 335-347, (2002) · Zbl 1009.47002 [7] Koliha, J.J.; Rakocevic, V., Holomorphic and meromorphic properties of the g-Drazin inverse, Demonstratio Mathematica, 38, 657-666, (2005) · Zbl 1092.47001 [8] Koliha, J.J.; Rakocevic, V., Differentiability of the g-Drazin inverse, Stud. math., 168, 193-201, (2005) · Zbl 1071.47019 [9] Djordjević, D.S.; Wei, Y., Additive results for the generalized Drazin inverse, J. austral. math. soc., 73, 115-125, (2002) · Zbl 1020.47001 [10] Castro González, N.; Koliha, J.J., New additive results for the g-Drazin inverse, Proc. roy. soc. Edinburgh sect. A, 134, 1085-1097, (2004) · Zbl 1088.15006 [11] Hartwig, R.E.; Wang, G.; Wei, Y., Some additive results on Drazin inverse, Linear algebra appl., 322, 207-217, (2001) · Zbl 0967.15003 [12] Meyer, C.D.; Rose, N.J., The index and the Drazin inverse of block triangular matrices, SIAM J. appl. math., 33, 1, 1-7, (1977) · Zbl 0355.15009 [13] Djordjević, D.S.; Stanimirović, P.S., On the generalized Drazin inverse and generalized resolvent, Czechoslovak math. J., 51, 126, 617-634, (2001) · Zbl 1079.47501 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.