Short geodesics of unitaries in the L2 metric

Autores
Andruchow, Esteban
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let M be a type II_1 von Neumann algebra,  τ a trace in M, and l^2 (M,τ) the GNS Hilbert space of τ. We regard the unitary group U_M as a subset of l^2 (M,τ), and characterize the shortest smooth curves of unitaries joining two fixed unitaries, in the L^2 metric. As a consequence of this we obtain that U_M, though a complete (metric) topological group, is not an embedded riemannian submanifold of l^2 (M,τ)
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
UNITARY GROUP
SHORT GEODESICS
INFINITE DIMENSIONAL RIEMANNIAN MANIFOLDS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/105166
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Short geodesics of unitaries in the L2 metricAndruchow, EstebanUNITARY GROUPSHORT GEODESICSINFINITE DIMENSIONAL RIEMANNIAN MANIFOLDShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let M be a type II_1 von Neumann algebra,  τ a trace in M, and l^2 (M,τ) the GNS Hilbert space of τ. We regard the unitary group U_M as a subset of l^2 (M,τ), and characterize the shortest smooth curves of unitaries joining two fixed unitaries, in the L^2 metric. As a consequence of this we obtain that U_M, though a complete (metric) topological group, is not an embedded riemannian submanifold of l^2 (M,τ)Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaCanadian Mathematical Soc2005-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/105166Andruchow, Esteban; Short geodesics of unitaries in the L2 metric; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 48; 3; 9-2005; 340-3540008-4395CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.4153/CMB-2005-032-0info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/short-geodesics-of-unitaries-in-the-l-2-metric/2212CACF3B2E3C2024CD2C3C2A390833info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-12T09:53:08Zoai:ri.conicet.gov.ar:11336/105166instacron: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:34982025-11-12 09:53:08.693CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Short geodesics of unitaries in the L2 metric
title Short geodesics of unitaries in the L2 metric
spellingShingle Short geodesics of unitaries in the L2 metric
Andruchow, Esteban
UNITARY GROUP
SHORT GEODESICS
INFINITE DIMENSIONAL RIEMANNIAN MANIFOLDS
title_short Short geodesics of unitaries in the L2 metric
title_full Short geodesics of unitaries in the L2 metric
title_fullStr Short geodesics of unitaries in the L2 metric
title_full_unstemmed Short geodesics of unitaries in the L2 metric
title_sort Short geodesics of unitaries in the L2 metric
dc.creator.none.fl_str_mv Andruchow, Esteban
author Andruchow, Esteban
author_facet Andruchow, Esteban
author_role author
dc.subject.none.fl_str_mv UNITARY GROUP
SHORT GEODESICS
INFINITE DIMENSIONAL RIEMANNIAN MANIFOLDS
topic UNITARY GROUP
SHORT GEODESICS
INFINITE DIMENSIONAL RIEMANNIAN MANIFOLDS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let M be a type II_1 von Neumann algebra,  τ a trace in M, and l^2 (M,τ) the GNS Hilbert space of τ. We regard the unitary group U_M as a subset of l^2 (M,τ), and characterize the shortest smooth curves of unitaries joining two fixed unitaries, in the L^2 metric. As a consequence of this we obtain that U_M, though a complete (metric) topological group, is not an embedded riemannian submanifold of l^2 (M,τ)
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description Let M be a type II_1 von Neumann algebra,  τ a trace in M, and l^2 (M,τ) the GNS Hilbert space of τ. We regard the unitary group U_M as a subset of l^2 (M,τ), and characterize the shortest smooth curves of unitaries joining two fixed unitaries, in the L^2 metric. As a consequence of this we obtain that U_M, though a complete (metric) topological group, is not an embedded riemannian submanifold of l^2 (M,τ)
publishDate 2005
dc.date.none.fl_str_mv 2005-09
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/11336/105166
Andruchow, Esteban; Short geodesics of unitaries in the L2 metric; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 48; 3; 9-2005; 340-354
0008-4395
CONICET Digital
CONICET
url http://hdl.handle.net/11336/105166
identifier_str_mv Andruchow, Esteban; Short geodesics of unitaries in the L2 metric; Canadian Mathematical Soc; Canadian Mathematical Bulletin-bulletin Canadien de Mathematiques; 48; 3; 9-2005; 340-354
0008-4395
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.4153/CMB-2005-032-0
info:eu-repo/semantics/altIdentifier/url/https://www.cambridge.org/core/journals/canadian-mathematical-bulletin/article/short-geodesics-of-unitaries-in-the-l-2-metric/2212CACF3B2E3C2024CD2C3C2A390833
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
dc.publisher.none.fl_str_mv Canadian Mathematical Soc
publisher.none.fl_str_mv Canadian Mathematical Soc
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 12.976206

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