环中和的群可逆性及其应用

Pub Date : 2024-03-25 DOI:10.1515/gmj-2024-2010

Huanyin Chen, Dayong Liu, Marjan Sheibani

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引用次数: 0

摘要

我们提出了环中两个群可逆元素之和是群可逆的必要条件和充分条件。作为应用，我们建立了巴拿赫空间上某些 2 × 2 {2\times 2} 块操作矩阵的群逆存在性。这些结果概括了已知结果，如 Zhou, Chen and Zhu (Comm.代数 48 (2020), 676-690) 和 Benítez、Liu 和 Zhu (Linear Multilinear Algebra 59 (2011), 279-289).

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Group invertibility of the sum in rings and its applications

We present necessary and sufficient conditions under which the sum of two group invertible elements in a ring is group invertible. As applications, we establish the existence of group inverses of certain 2 × 2

{2\times 2}

block-operator matrices over a Banach space. These generalize the known results, e.g., Zhou, Chen and Zhu (Comm. Algebra 48 (2020), 676–690) and Benítez, Liu and Zhu (Linear Multilinear Algebra 59 (2011), 279–289).

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