English

Group invertibility of the sum in rings and its applications

Rings and Algebras 2022-03-16 v1

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 2×22\times 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).

Keywords

Cite

@article{arxiv.2203.07582,
  title  = {Group invertibility of the sum in rings and its applications},
  author = {Huanyin Chen and Dayong Liu and Marjan Sheibani},
  journal= {arXiv preprint arXiv:2203.07582},
  year   = {2022}
}