The $(b, c)$-inverse in rings and in the Banach context
Abstract
In this article the -inverse will be studied. Several equivalent conditions for the existence of the -inverse in rings will be given. In particular, the conditions ensuring the existence of the -inverse, of the annihilator -inverse and of the hybrid -inverse will be proved to be equivalent, provided and are regular elements in a unitary ring . In addition, the set of all -invertible elements will be characterized and the reverse order law will be also studied. Moreover, the relationship between the -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 -inverse will be characterized
Cite
@article{arxiv.1607.02456,
title = {The $(b, c)$-inverse in rings and in the Banach context},
author = {Enrico Boasso and Gabriel Kantun-Montiel},
journal= {arXiv preprint arXiv:1607.02456},
year = {2016}
}
Comments
20 pages, original research article