The group inverse of the sum in a Banach algebra
Functional Analysis
2022-03-16 v1 Rings and Algebras
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 \cite{L}.
Keywords
Cite
@article{arxiv.2203.07683,
title = {The group inverse of the sum in a Banach algebra},
author = {Huanyin Chen and Marjan Sheibani},
journal= {arXiv preprint arXiv:2203.07683},
year = {2022}
}