RT journal article
T1 Invertibles in topological rings: A new approach
A1 García Pacheco, Francisco Javier
A1 Miralles, A.
A1 Murillo Arcila, Marina
A2 Matemáticas
K1 Spectrum
K1 Rings
K1 Algebras
K1 Zero divisor
K1 Invertibles
K1 Operator
AB Every element in the boundary of the group of invertibles of a Banach algebra is a topologicalzero divisor. We extend this result to the scope of topological rings. In particular, wedefine a new class of semi-normed rings, called almost absolutely semi-normed rings, whichstrictly includes the class of absolutely semi-valued rings, and prove that every element inthe boundary of the group of invertibles of a complete almost absolutely semi-normed ringis a topological zero divisor. To achieve all these, we have to previously entail an exhaustivestudy of topological divisors of zero in topological rings. In addition, it is also well knownthat the group of invertibles is open and the inversion map is continuous and C-differentiablein a Banach algebra. We also extend these results to the setting of complete normed rings.Finally, this study allows us to generalize the point, continuous and residual spectra to thescope of Banach algebras.
PB Springer
SN 1579-1505
YR 2022
FD 2022
LK http://hdl.handle.net/10498/35343
UL http://hdl.handle.net/10498/35343
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 21-sep-2026