Geodesic
The g-Drazin inverse involving power commutativity
Filomat, Tome 34 (2020) no. 9, p. 2961

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DOI

Let A be a complex Banach algebra. An element a ∈ A has g-Drazin inverse if there exists b ∈ A such that b = bab, ab = ba, a − a 2 b ∈ A qnil. Let a, b ∈ A d. If a 3 b = ba, b 3 a = ab, and a 2 a d b = aa d ba, we prove that a + b ∈ A d if and only if 1 + a d b ∈ A d. We present explicit formula for (a + b) d under certain perturbations. These extend the main results of Wang, Zhou and Chen (Filomat, 30(2016), 1185–1193) and Liu, Xu and Yu (Applied Math. Comput., 216(2010), 3652–3661).
DOI : 10.2298/FIL2009961C
Classification : 15A09, 47L10, 32A65
Keywords: g-Drazin inverse, additive property, perturbation, Banach algebra 
Huanyin Chen; Marjan Sheibani; Handan Kose. The g-Drazin inverse involving power commutativity. Filomat, Tome 34 (2020) no. 9, p. 2961 . doi: 10.2298/FIL2009961C
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     title = {The {g-Drazin} inverse involving power commutativity},
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     doi = {10.2298/FIL2009961C},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2009961C/}
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