Geodesic
New characterizations of g-Drazin inverse in a Banach algebra
Filomat, Tome 37 (2023) no. 6, p. 1803

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DOI

In this paper, we present a new characterization of g-Drazin inverse in a Banach algebra. We prove that an element a in a Banach algebra has g-Drazin inverse if and only if there exists x ∈ A such that ax = xa, a− a2x ∈ Aqnil. As an application, we obtain the sufficient and necessary conditions for the existence of the g-Drazin inverse for certain 2 × 2 anti-triangular matrices over a Banach algebra. These extend the results of Koliha (Glasgow Math. J. 38(1996), 367-381), Nicholson (Comm. Algebra, 27(1999), 3583-3592 and Zou et al. (Studia Scient. Math. Hungar., 54(2017), 489-508).
DOI : 10.2298/FIL2306803C
Classification : 15A09, 32A65
Keywords: g-Drazin inverse, Anti-triangular matrix, Banach algebra 
Huanyin Chen; Marjan Sheibani Abdolyousefi. New characterizations of g-Drazin inverse in a Banach algebra. Filomat, Tome 37 (2023) no. 6, p. 1803 . doi: 10.2298/FIL2306803C
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     title = {New characterizations of {g-Drazin} inverse in a {Banach} algebra},
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