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arXiv · 1607.02456

The $(b, c)$-inverse in rings and in the Banach context

Enrico Boasso·Gabriel Kantun-Montiel
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Abstract

In this article the $(b, c)$-inverse will be studied. Several equivalent conditions for the existence of the $(b,c)$-inverse in rings will be given. In particular, the conditions ensuring the existence of the $(b,c)$-inverse, of the annihilator $(b,c)$-inverse and of the hybrid $(b,c)$-inverse will be proved to be equivalent, provided $b$ and $c$ are regular elements in a unitary ring $R$. In addition, the set of all $(b,c)$-invertible elements will be characterized and the reverse order law will be also studied. Moreover, the relationship between the $(b,c)$-inverse and the Bott-Duffin inverse will be considered. In the context of Banach algebras, integral, series and limit representations will be given. Finally the continuity of the $(b,c)$-inverse will be characterized

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Enrico Boasso, Gabriel Kantun-Montiel. 2016-07-08. The $(b, c)$-inverse in rings and in the Banach context. https://arxiv.org/abs/1607.02456

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