Topological dimension zero and some related properties

In this paper, we introduce and study the C*-algebras with property (IC) and with other related properties. We prove that, surprisingly, residual (IC) is equivalent to topological dimension zero (and to another property), and that in the class of C*-algebras with topological dimension zero, pure inf...

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Detalles Bibliográficos
Autores: Pasnicu, Cornel|||0000-0002-0209-0965, Rouzbehani, Mohammad
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:318137
Acceso en línea:https://ddd.uab.cat/record/318137
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922506
Access Level:acceso abierto
Palabra clave:C*-algebra
Residual (ic)
Topological dimension zero
(strongly, weakly, locally) purely infinite
The (weak) ideal property
Crossed product
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spelling Topological dimension zero and some related propertiesPasnicu, Cornel|||0000-0002-0209-0965Rouzbehani, MohammadC*-algebraResidual (ic)Topological dimension zero(strongly, weakly, locally) purely infiniteThe (weak) ideal propertyCrossed productIn this paper, we introduce and study the C*-algebras with property (IC) and with other related properties. We prove that, surprisingly, residual (IC) is equivalent to topological dimension zero (and to another property), and that in the class of C*-algebras with topological dimension zero, pure infiniteness and strong pure infiniteness coincide, providing a partial positive answer to a question of Kirchberg and Rørdam in [12]. We also show that these last two properties are equivalent to weak pure infiniteness and to local pure infiniteness, in the residual (IS) case, giving a particular affirmative answer to an open question of Blanchard and Kirchberg in [2]. We prove, in particular, that in the class of purely infinite C*-algebras, the following properties are all equivalent: residual (IC), topological dimension zero, the ideal property, the weak ideal property, residual (IF), and residual (SP). We show that crossed products by finite solvable groups preserve the class of all separable C*-algebras with topological dimension zero (resp., the weak ideal property). 22025-01-0120252025-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/318137https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922506reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:3181372026-06-06T12:50:31Z
dc.title.none.fl_str_mv Topological dimension zero and some related properties
title Topological dimension zero and some related properties
spellingShingle Topological dimension zero and some related properties
Pasnicu, Cornel|||0000-0002-0209-0965
C*-algebra
Residual (ic)
Topological dimension zero
(strongly, weakly, locally) purely infinite
The (weak) ideal property
Crossed product
title_short Topological dimension zero and some related properties
title_full Topological dimension zero and some related properties
title_fullStr Topological dimension zero and some related properties
title_full_unstemmed Topological dimension zero and some related properties
title_sort Topological dimension zero and some related properties
dc.creator.none.fl_str_mv Pasnicu, Cornel|||0000-0002-0209-0965
Rouzbehani, Mohammad
author Pasnicu, Cornel|||0000-0002-0209-0965
author_facet Pasnicu, Cornel|||0000-0002-0209-0965
Rouzbehani, Mohammad
author_role author
author2 Rouzbehani, Mohammad
author2_role author
dc.subject.none.fl_str_mv C*-algebra
Residual (ic)
Topological dimension zero
(strongly, weakly, locally) purely infinite
The (weak) ideal property
Crossed product
topic C*-algebra
Residual (ic)
Topological dimension zero
(strongly, weakly, locally) purely infinite
The (weak) ideal property
Crossed product
description In this paper, we introduce and study the C*-algebras with property (IC) and with other related properties. We prove that, surprisingly, residual (IC) is equivalent to topological dimension zero (and to another property), and that in the class of C*-algebras with topological dimension zero, pure infiniteness and strong pure infiniteness coincide, providing a partial positive answer to a question of Kirchberg and Rørdam in [12]. We also show that these last two properties are equivalent to weak pure infiniteness and to local pure infiniteness, in the residual (IS) case, giving a particular affirmative answer to an open question of Blanchard and Kirchberg in [2]. We prove, in particular, that in the class of purely infinite C*-algebras, the following properties are all equivalent: residual (IC), topological dimension zero, the ideal property, the weak ideal property, residual (IF), and residual (SP). We show that crossed products by finite solvable groups preserve the class of all separable C*-algebras with topological dimension zero (resp., the weak ideal property).
publishDate 2025
dc.date.none.fl_str_mv 2
2025-01-01
2025
2025-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/318137
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922506
url https://ddd.uab.cat/record/318137
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6922506
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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