Group invertibility of the sum in rings and its applications

2022/03/15 by Chen, Huanyin, Liu, Dayong, Sheibani, Marjan · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2203.07582

Abstract

We present new additive results for the group invertibility in a ring. Then we apply our results to block operator matrices over Banach spaces and derive the existence of group inverses of 2× 2 block operator matrices. These generalize many known results, e.g., Benitez, Liu and Zhu(Linear Multilinear Algebra, \bf 59(2011), 279--289) and Zhou, Chen and Zhu(Comm. Algebra, \bf 48(2020),676-690).

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• The m-generalized right group inverses in Banach algebras

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