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arXiv · 2203.07683

The group inverse of the sum in a Banach algebra

Huanyin Chen·Marjan Sheibani
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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}.

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Huanyin Chen, Marjan Sheibani. 2022-03-15. The group inverse of the sum in a Banach algebra. https://arxiv.org/abs/2203.07683

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