Geodesic
Some additive results for the generalized Drazin inverse in a Banach algebra
The electronic journal of linear algebra, Tome 22 (2011), pp. 1049-1058.

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Summary: In this note, additive results are presented for the generalized Drazin inverse in Ba- nach algebra. Necessary and sufficient conditions are given for the generalized Drazin invertibility of the sum of two commuting generalized Drazin invertible elements. These results are a generalization of the results from the paper [C.Y. Deng and Y. Wei. New additive results for the generalized Drazin inverse. J. Math. Anal. Appl., 370:313-321, 2010.] to the Banach algebra case.
Classification : 15A09
Keywords: Banach algebra, generalized Drazin inverse, additive properties 
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     title = {Some additive results for the generalized {Drazin} inverse in a {Banach} algebra},
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Cvetkovic-Ilic, Dragana S.; Liu, Xiaoji; Wei, Yimin. Some additive results for the generalized Drazin inverse in a Banach algebra. The electronic journal of linear algebra, Tome 22 (2011), pp. 1049-1058. http://geodesic.mathdoc.fr/item/ELA_2011__22__a9/