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arXiv · 2009.02477

New characterizations of G-Drazin inverse in Banach algebra

Huanyin Chen·Marjan Sheibani Abdolyousefi
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Abstract

In this paper, we present a new characterization of g-Drazin inverse in a Banach algebra. We prove that an element a is a Banach algebra has g-Drazin inverse if and only if there exists $x\in A$ such that $ax=xa, a-a^2x\in A^{qnil}$. we obtain the sufficient and necessary conditions for the existence of the g-Drain inverse for certain $2 \times 2$ 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).

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Huanyin Chen, Marjan Sheibani Abdolyousefi. 2020-09-05. New characterizations of G-Drazin inverse in Banach algebra. https://arxiv.org/abs/2009.02477

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