%0 Journal Article 
%A García Pacheco, Francisco Javier
%A Moreno Frías, María Ángeles
%A Murillo Arcila, Marina
%T On absolutely invertibles
%D 2025
%@ 2688-1594
%U http://hdl.handle.net/10498/34357
%X 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.
%K ∗-ring
%K absolutely invertible
%K topological ring
%K normal subgroup
%~ Universidad de Cádiz