Amenable traces and Følner C*-algebras

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dc.contributor.author Ara, Pere
dc.contributor.author Lledó Macau, Fernando
dc.date.accessioned 2016-07-19T10:53:54Z
dc.date.available 2017-01-01T23:00:06Z
dc.date.issued 2014
dc.identifier.bibliographicCitation Expositiones Mathematicae, 2014, v. 32, Issue 2, pp. 161-177
dc.identifier.issn 0723-0869
dc.identifier.uri http://hdl.handle.net/10016/23377
dc.description.abstract In the present article we review an approximation procedure for amenable traces on unital andseparable C*-algebras acting on a Hilbert space in terms of Følner sequences of non-zero finite rankprojections. We apply this method to improve spectral approximation results due to Arveson and Bédos. We also present an abstract characterization in terms of unital completely positive maps ofunital separable C*-algebras admitting a non-degenerate representation which has a Følner sequenceor, equivalently, an amenable trace. This is analogous to Voiculescu's abstract characterization ofquasidiagonal C*-algebras. We define Følner C*-algebras as those unital separable C*-algebras thatsatisfy these equivalent conditions. Finally we also mention some permanence properties related tothese algebras.
dc.description.sponsorship The first author was partially supported by DGI MICIIN MTM2011-28992-C02-01, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The second author was partially supported by projects DGI MICIIN MTM2012-36372-C03-01 and Severo Ochoa SEV-2011-0087 of the Spanish Ministry of Economy and Competition.
dc.format.extent 18
dc.format.mimetype application/pdf
dc.language.iso eng
dc.publisher Elsevier
dc.rights © Elsevier 2014
dc.rights Atribución-NoComercial-SinDerivadas 3.0 España
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.other C-algebras
dc.subject.other Folner sequences
dc.subject.other Amenable groups
dc.subject.other Amenable trace
dc.subject.other Crossed products
dc.subject.other Tensor products
dc.title Amenable traces and Følner C*-algebras
dc.type article
dc.relation.publisherversion http://dx.doi.org/10.1016/j.exmath.2013.10.002
dc.subject.eciencia Matemáticas
dc.identifier.doi 10.1016/j.exmath.2013.10.002
dc.rights.accessRights openAccess
dc.relation.projectID Gobierno de España. MTM2012-36372-C03-01
dc.relation.projectID Gobierno de España. SEV-2011-0087
dc.type.version acceptedVersion
dc.identifier.publicationfirstpage 161
dc.identifier.publicationissue 2
dc.identifier.publicationlastpage 177
dc.identifier.publicationtitle Expositiones mathematicae
dc.identifier.publicationvolume 32
dc.identifier.uxxi AR/0000018015
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