The group inverse of the sum in a Banach algebra

2022/03/15 by Huanyin Chen, Chen, Huanyin, Marjan Sheibani +1
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #math.FA #math.RA

paper · pdf · doi:10.48550/arxiv.2203.07683

arxiv created 2022/03/15 · openalex publication_date 2022/03/15 · arxiv updated 2022/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we present new necessary and sufficient conditions under which the sum of two group invertible elements in a Banach algebra has group inverse. We then apply these results to block operator matrices over Banach spaces. The group inverses of certain operator block matrices are thereby obtained. Additionally, this paper extends the results obtained in \citeL.

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