Unitarization of uniformly bounded subgroups in finite von Neumann algebras

Autores
Miglioli, Martín Carlos
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This note presents a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. In 1974, Vasilescu and Zsido proved this result using the Ryll-Nardzewsky fixed point theorem [Vasilescu and Zsido, "Uniformly bounded groups in finite W*-algebras", Acta Sci. Math. (Szeged) 36 (1974) 189-192]. This new proof involves metric geometric arguments in the non-positively curved space of positive invertible operators of the algebra, which yield a more explicit unitarizer.
Fil: Miglioli, Martín Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Materia
Bounded subgroup
Finite algebra
Nonposite curvature
Unitarization
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
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Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
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spelling Unitarization of uniformly bounded subgroups in finite von Neumann algebrasMiglioli, Martín CarlosBounded subgroupFinite algebraNonposite curvatureUnitarizationhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This note presents a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. In 1974, Vasilescu and Zsido proved this result using the Ryll-Nardzewsky fixed point theorem [Vasilescu and Zsido, "Uniformly bounded groups in finite W*-algebras", Acta Sci. Math. (Szeged) 36 (1974) 189-192]. This new proof involves metric geometric arguments in the non-positively curved space of positive invertible operators of the algebra, which yield a more explicit unitarizer.Fil: Miglioli, Martín Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaOxford University Press2014-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18951Miglioli, Martín Carlos; Unitarization of uniformly bounded subgroups in finite von Neumann algebras; Oxford University Press; Bulletin Of The London Mathematical Society; 46; 6; 12-2014; 1264-12660024-6093CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/blms/bdu080/fullinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1302.7303info:eu-repo/semantics/altIdentifier/doi/10.1112/blms/bdu080info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:30:39Zoai:ri.conicet.gov.ar:11336/18951instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:30:40.124CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Unitarization of uniformly bounded subgroups in finite von Neumann algebras
title Unitarization of uniformly bounded subgroups in finite von Neumann algebras
spellingShingle Unitarization of uniformly bounded subgroups in finite von Neumann algebras
Miglioli, Martín Carlos
Bounded subgroup
Finite algebra
Nonposite curvature
Unitarization
title_short Unitarization of uniformly bounded subgroups in finite von Neumann algebras
title_full Unitarization of uniformly bounded subgroups in finite von Neumann algebras
title_fullStr Unitarization of uniformly bounded subgroups in finite von Neumann algebras
title_full_unstemmed Unitarization of uniformly bounded subgroups in finite von Neumann algebras
title_sort Unitarization of uniformly bounded subgroups in finite von Neumann algebras
dc.creator.none.fl_str_mv Miglioli, Martín Carlos
author Miglioli, Martín Carlos
author_facet Miglioli, Martín Carlos
author_role author
dc.subject.none.fl_str_mv Bounded subgroup
Finite algebra
Nonposite curvature
Unitarization
topic Bounded subgroup
Finite algebra
Nonposite curvature
Unitarization
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This note presents a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. In 1974, Vasilescu and Zsido proved this result using the Ryll-Nardzewsky fixed point theorem [Vasilescu and Zsido, "Uniformly bounded groups in finite W*-algebras", Acta Sci. Math. (Szeged) 36 (1974) 189-192]. This new proof involves metric geometric arguments in the non-positively curved space of positive invertible operators of the algebra, which yield a more explicit unitarizer.
Fil: Miglioli, Martín Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
description This note presents a new proof of the fact that every uniformly bounded group of invertible elements in a finite von Neumann algebra is similar to a unitary group. In 1974, Vasilescu and Zsido proved this result using the Ryll-Nardzewsky fixed point theorem [Vasilescu and Zsido, "Uniformly bounded groups in finite W*-algebras", Acta Sci. Math. (Szeged) 36 (1974) 189-192]. This new proof involves metric geometric arguments in the non-positively curved space of positive invertible operators of the algebra, which yield a more explicit unitarizer.
publishDate 2014
dc.date.none.fl_str_mv 2014-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/18951
Miglioli, Martín Carlos; Unitarization of uniformly bounded subgroups in finite von Neumann algebras; Oxford University Press; Bulletin Of The London Mathematical Society; 46; 6; 12-2014; 1264-1266
0024-6093
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18951
identifier_str_mv Miglioli, Martín Carlos; Unitarization of uniformly bounded subgroups in finite von Neumann algebras; Oxford University Press; Bulletin Of The London Mathematical Society; 46; 6; 12-2014; 1264-1266
0024-6093
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://onlinelibrary.wiley.com/doi/10.1112/blms/bdu080/full
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1302.7303
info:eu-repo/semantics/altIdentifier/doi/10.1112/blms/bdu080
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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