RT journal article
T1 On absolutely invertibles
A1 García Pacheco, Francisco Javier
A1 Moreno Frías, María Ángeles
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 ∗-ring
K1 absolutely invertible
K1 topological ring
K1 normal subgroup
AB 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.
SN 2688-1594
YR 2025
FD 2025
LK http://hdl.handle.net/10498/34357
UL http://hdl.handle.net/10498/34357
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 11-nov-2026