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A noncommutative Amir-Cambern theorem for von Neumann algebras and nuclear ${C}^∗$-algebras.

hal.structure.identifierLaboratoire de Mathématiques de Besançon (UMR 6623) [LMB]
hal.structure.identifierLaboratoire de Mathématiques Nicolas Oresme [LMNO]
dc.contributor.authorRICARD, Éric
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorROYDOR, Jean
dc.date.accessioned2024-04-04T03:22:10Z
dc.date.available2024-04-04T03:22:10Z
dc.date.created2013
dc.date.issued2014
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/194730
dc.description.abstractEnWe prove that von Neumann algebras and separable nuclear $C^∗$ -algebras are stable for the Banach-Mazur cb-distance. A technical step is to show that unital almost completely isometric maps between $C^∗$ -algebras are almost multiplicative and almost selfadjoint. Also as an intermediate result, we compare the Banach-Mazur cb-distance and the Kadison-Kastler distance. Finally, we show that if two $C^∗$ -algebras are close enough for the cb-distance, then they have at most the same length.
dc.language.isoen
dc.title.enA noncommutative Amir-Cambern theorem for von Neumann algebras and nuclear ${C}^∗$-algebras.
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Analyse fonctionnelle [math.FA]
bordeaux.journalJ. Funct. Anal. 267 (2014)
bordeaux.pageJ. Funct. Anal. 267 (2014), no. 4, 1121-1136.
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01016334
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01016334v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=J.%20Funct.%20Anal.%20267%20(2014)&rft.date=2014&rft.spage=J.%20Funct.%20Anal.%20267%20(2014),%20no.%204,%201121-1136.&rft.epage=J.%20Funct.%20Anal.%20267%20(2014),%20no.%204,%201121-1136.&rft.au=RICARD,%20%C3%89ric&ROYDOR,%20Jean&rft.genre=article


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