New characterizations of g-Drazin inverse in a Banach algebra

被引：0

作者：

Chen, Huanyin ^{[1
]}

Abdolyousefi, Marjan Sheibani ^{[2
]}

机构：

[1] Hangzhou Normal Univ, Sch Math, Hangzhou, Peoples R China

[2] Semnan Univ, Farzanegan Campus, Semnan, Iran

来源：

FILOMAT | 2023年 / 37卷 / 06期

关键词：

g-Drazin inverse; Anti-triangular matrix; Banach algebra; CLINES FORMULA; INVERTIBILITY; MATRICES;

D O I：

10.2298/FIL2306803C

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 E 51 such that ax = xa, a - a2x E 51qnil. As an application, we obtain the sufficient and necessary conditions for the existence of the g-Drazin inverse for certain 2 x 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).

引用

页码：1803 / 1813

页数：11

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