Ontology type: schema:ScholarlyArticle Open Access: True
2021-11-15
AUTHORSFrancisco Javier García-Pacheco, Alejandro Miralles, Marina Murillo-Arcila
ABSTRACTEvery 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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}$$\end{document}-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. More... »
PAGES38
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
ISSUE1
VOLUME116
http://scigraph.springernature.com/pub.10.1007/s13398-021-01183-4
DOIhttp://dx.doi.org/10.1007/s13398-021-01183-4
DIMENSIONShttps://app.dimensions.ai/details/publication/pub.1142599545
JSON-LD is the canonical representation for SciGraph data.
TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT
[
{
"@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json",
"about": [
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Mathematical Sciences",
"type": "DefinedTerm"
},
{
"id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101",
"inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/",
"name": "Pure Mathematics",
"type": "DefinedTerm"
}
],
"author": [
{
"affiliation": {
"alternateName": "Departamento de Matem\u00e1ticas, Escuela Superior de Ingenier\u00eda, Universidad de C\u00e1diz, 11510, Puerto Real, Spain",
"id": "http://www.grid.ac/institutes/grid.7759.c",
"name": [
"Departamento de Matem\u00e1ticas, Escuela Superior de Ingenier\u00eda, Universidad de C\u00e1diz, 11510, Puerto Real, Spain"
],
"type": "Organization"
},
"familyName": "Garc\u00eda-Pacheco",
"givenName": "Francisco Javier",
"id": "sg:person.016046240355.05",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016046240355.05"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "IMAC and Departament de Matem\u00e0tiques, Universitat Jaume I, 12071, Castell\u00f3 de la Plana, Spain",
"id": "http://www.grid.ac/institutes/grid.9612.c",
"name": [
"IMAC and Departament de Matem\u00e0tiques, Universitat Jaume I, 12071, Castell\u00f3 de la Plana, Spain"
],
"type": "Organization"
},
"familyName": "Miralles",
"givenName": "Alejandro",
"id": "sg:person.014556720503.09",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014556720503.09"
],
"type": "Person"
},
{
"affiliation": {
"alternateName": "Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022, Val\u00e8ncia, Spain",
"id": "http://www.grid.ac/institutes/grid.157927.f",
"name": [
"Instituto Universitario de Matem\u00e1tica Pura y Aplicada, Universitat Polit\u00e8cnica de Val\u00e8ncia, 46022, Val\u00e8ncia, Spain"
],
"type": "Organization"
},
"familyName": "Murillo-Arcila",
"givenName": "Marina",
"id": "sg:person.014325141701.62",
"sameAs": [
"https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014325141701.62"
],
"type": "Person"
}
],
"citation": [
{
"id": "sg:pub.10.1007/978-3-7643-8265-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1008754231",
"https://doi.org/10.1007/978-3-7643-8265-0"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-0-85729-183-7",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1019294674",
"https://doi.org/10.1007/978-0-85729-183-7"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s13398-014-0168-4",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1009893860",
"https://doi.org/10.1007/s13398-014-0168-4"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4757-4090-5",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1109705759",
"https://doi.org/10.1007/978-1-4757-4090-5"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/s43037-020-00055-0",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1124837451",
"https://doi.org/10.1007/s43037-020-00055-0"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-3-642-66282-9",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1016619032",
"https://doi.org/10.1007/978-3-642-66282-9"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.15352/bjma/09-4-12",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1067742105",
"https://doi.org/10.15352/bjma/09-4-12"
],
"type": "CreativeWork"
},
{
"id": "sg:pub.10.1007/978-1-4612-0603-3",
"sameAs": [
"https://app.dimensions.ai/details/publication/pub.1053355415",
"https://doi.org/10.1007/978-1-4612-0603-3"
],
"type": "CreativeWork"
}
],
"datePublished": "2021-11-15",
"datePublishedReg": "2021-11-15",
"description": "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\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\mathbb {C}$$\\end{document}-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.",
"genre": "article",
"id": "sg:pub.10.1007/s13398-021-01183-4",
"inLanguage": "en",
"isAccessibleForFree": true,
"isPartOf": [
{
"id": "sg:journal.1136515",
"issn": [
"1578-7303",
"1579-1505"
],
"name": "Revista de la Real Academia de Ciencias Exactas, F\u00edsicas y Naturales. Serie A. Matem\u00e1ticas",
"publisher": "Springer Nature",
"type": "Periodical"
},
{
"issueNumber": "1",
"type": "PublicationIssue"
},
{
"type": "PublicationVolume",
"volumeNumber": "116"
}
],
"keywords": [
"group of invertibles",
"Banach algebra",
"topological ring",
"topological divisors",
"normed rings",
"algebra",
"invertibles",
"divisors",
"inversion map",
"new class",
"new approach",
"class",
"residual spectrum",
"exhaustive study",
"boundaries",
"ring",
"point",
"results",
"approach",
"elements",
"spectra",
"maps",
"scope",
"addition",
"setting",
"study",
"group"
],
"name": "Invertibles in topological rings: a new approach",
"pagination": "38",
"productId": [
{
"name": "dimensions_id",
"type": "PropertyValue",
"value": [
"pub.1142599545"
]
},
{
"name": "doi",
"type": "PropertyValue",
"value": [
"10.1007/s13398-021-01183-4"
]
}
],
"sameAs": [
"https://doi.org/10.1007/s13398-021-01183-4",
"https://app.dimensions.ai/details/publication/pub.1142599545"
],
"sdDataset": "articles",
"sdDatePublished": "2022-05-20T07:37",
"sdLicense": "https://scigraph.springernature.com/explorer/license/",
"sdPublisher": {
"name": "Springer Nature - SN SciGraph project",
"type": "Organization"
},
"sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_889.jsonl",
"type": "ScholarlyArticle",
"url": "https://doi.org/10.1007/s13398-021-01183-4"
}
]Download the RDF metadata as: json-ld nt turtle xml License info
JSON-LD is a popular format for linked data which is fully compatible with JSON.
curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s13398-021-01183-4'
N-Triples is a line-based linked data format ideal for batch operations.
curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s13398-021-01183-4'
Turtle is a human-readable linked data format.
curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s13398-021-01183-4'
RDF/XML is a standard XML format for linked data.
curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s13398-021-01183-4'
This table displays all metadata directly associated to this object as RDF triples.
137 TRIPLES
22 PREDICATES
60 URIs
44 LITERALS
6 BLANK NODES