Invertibles in topological rings: a new approach
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
Invertibles in topological rings: a new approachDate
2021-11-15Publisher
SpringerBibliographic citation
García-Pacheco, F.J., Miralles, A. & Murillo-Arcila, M. Invertibles in topological rings: a new approach. RACSAM 116, 38 (2022). https://doi.org/10.1007/s13398-021-01183-4Type
info:eu-repo/semantics/articleVersion
info:eu-repo/semantics/publishedVersionSubject
Abstract
Every element in the boundary of the group of invertibles of a Banach algebra is a topological zero divisor. We extend this result to the scope of topological rings. In particular, we
define a new class of semi-normed ... [+]
Every element in the boundary of the group of invertibles of a Banach algebra is a topological zero divisor. We extend this result to the scope of topological rings. In particular, we
define a new class of semi-normed rings, called almost absolutely semi-normed rings, which
strictly includes the class of absolutely semi-valued rings, and prove that every element in
the boundary of the group of invertibles of a complete almost absolutely semi-normed ring
is a topological zero divisor. To achieve all these, we have to previously entail an exhaustive
study of topological divisors of zero in topological rings. In addition, it is also well known
that the group of invertibles is open and the inversion map is continuous and C-differentiable
in 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 the
scope of Banach algebras. [-]
Is part of
RACSAM (2022) 116Funder Name
Ministerio de Ciencia, Innovación y Universidades (Spain) | Regional Government of Andalusia. Department of Economy, Knowledge, Business and University | Ministerio de Educación y Ciencia (Spain) | Universitat Jaume I | Generalitat Valenciana
Project code
PGC-101514-B-I00 | FEDER-UCA18-105867 | MTM2016- 75963-P | PGC2018-094431-B-100 | 8059/2019 | MCIN/AEI/10.13039/501100011033 | PID2019-105011GB-I00 | PROMETEU/2021/070
Project title or grant
2014-2020 ERDF Operational Programme
Rights
© The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2021
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info:eu-repo/semantics/openAccess
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info:eu-repo/semantics/openAccess
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