@misc{10498/34357,
year = {2025},
url = {http://hdl.handle.net/10498/34357},
abstract = {In this manuscript,the notion of absolutely invertible was extended consistently froms semi-normed rings to the class of general topological rings. Then, the closure of the absolutely invertibles multiplied by a certain element was proved to be contained in the set of topological divisors of the element. Also, a sufficient condition for the closed unit ball of a complete unital normed ring to become a closed unit neighborhood of zero was found. Finally, two applications to classical operator theory were provided, i.e., every Banach space of dimension of at least 2 could be equivalently re-normed in such a way that the group of surjective linear isometries was not a normal subgroup of the group of isomorphisms, and every infinite-dimensional Banach space, containing a proper complemented subspace isomorphic to it, could be equivalently re-normed so that the set of surjective linear operators was not dense in the Banach algebra of bounded linear operators.},
keywords = {∗-ring},
keywords = {absolutely invertible},
keywords = {topological ring},
keywords = {normal subgroup},
title = {On absolutely invertibles},
doi = {10.3934/ERA.2024307},
author = {García Pacheco, Francisco Javier and Moreno Frías, María Ángeles and Murillo Arcila, Marina},
}