Examples of homogeneous manifolds with uniformly bounded metric projection

Let M be a finite von Neumann algebra with a faithful normal trace τ. Denote by Lp(M)sh the skew-Hermitian part of the non-commutative Lp space associated with (M, τ). Let 1 < p < ∞, z ∈ Lp(M)sh and S be a real closed subspace of Lp(M)sh. The metric projection Q : Lp(M)sh −→ S is defined for e...

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Detalles Bibliográficos
Autor: Chiumiento, Eduardo Hernan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/18935
Acceso en línea:http://hdl.handle.net/11336/18935
Access Level:acceso abierto
Palabra clave:finite von Neumann algebra
metric projection
homogeneous space
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
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spelling Examples of homogeneous manifolds with uniformly bounded metric projectionChiumiento, Eduardo Hernanfinite von Neumann algebrametric projectionhomogeneous spacehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let M be a finite von Neumann algebra with a faithful normal trace τ. Denote by Lp(M)sh the skew-Hermitian part of the non-commutative Lp space associated with (M, τ). Let 1 < p < ∞, z ∈ Lp(M)sh and S be a real closed subspace of Lp(M)sh. The metric projection Q : Lp(M)sh −→ S is defined for every z ∈ Lp(M)sh as the unique operator Q(z) ∈ S such that kz − Q(z)kp = miny∈ S kz − ykp. We show the relation between metric projection and metric geometry of homogeneous spaces of the unitary group UM of M, endowed with a Finsler quotient metric induced by the p-norms of τ, kxkp = τ(|x| p) 1/p, p an even integer. The problem of finding minimal curves in such homogeneous spaces leads to the notion of uniformly bounded metric projection. Then we show examples of metric projections of this type.Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Económicas; ArgentinaUnión Matemática Argentina2012-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/18935Chiumiento, Eduardo Hernan; Examples of homogeneous manifolds with uniformly bounded metric projection; Unión Matemática Argentina; Revista de la Union Matemática Argentina; 53; 2; 11-2012; 13-230041-69321669-9637CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.criba.edu.ar/revuma/pdf/v53n2/v53n2a02.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:42:42Zoai:ri.conicet.gov.ar:11336/18935instacron: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:34982024-05-08 13:42:42.491CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Examples of homogeneous manifolds with uniformly bounded metric projection
title Examples of homogeneous manifolds with uniformly bounded metric projection
spellingShingle Examples of homogeneous manifolds with uniformly bounded metric projection
Chiumiento, Eduardo Hernan
finite von Neumann algebra
metric projection
homogeneous space
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
title_short Examples of homogeneous manifolds with uniformly bounded metric projection
title_full Examples of homogeneous manifolds with uniformly bounded metric projection
title_fullStr Examples of homogeneous manifolds with uniformly bounded metric projection
title_full_unstemmed Examples of homogeneous manifolds with uniformly bounded metric projection
title_sort Examples of homogeneous manifolds with uniformly bounded metric projection
dc.creator.none.fl_str_mv Chiumiento, Eduardo Hernan
author Chiumiento, Eduardo Hernan
author_facet Chiumiento, Eduardo Hernan
author_role author
dc.subject.none.fl_str_mv finite von Neumann algebra
metric projection
homogeneous space
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
topic finite von Neumann algebra
metric projection
homogeneous space
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
description Let M be a finite von Neumann algebra with a faithful normal trace τ. Denote by Lp(M)sh the skew-Hermitian part of the non-commutative Lp space associated with (M, τ). Let 1 < p < ∞, z ∈ Lp(M)sh and S be a real closed subspace of Lp(M)sh. The metric projection Q : Lp(M)sh −→ S is defined for every z ∈ Lp(M)sh as the unique operator Q(z) ∈ S such that kz − Q(z)kp = miny∈ S kz − ykp. We show the relation between metric projection and metric geometry of homogeneous spaces of the unitary group UM of M, endowed with a Finsler quotient metric induced by the p-norms of τ, kxkp = τ(|x| p) 1/p, p an even integer. The problem of finding minimal curves in such homogeneous spaces leads to the notion of uniformly bounded metric projection. Then we show examples of metric projections of this type.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
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/11336/18935
Chiumiento, Eduardo Hernan; Examples of homogeneous manifolds with uniformly bounded metric projection; Unión Matemática Argentina; Revista de la Union Matemática Argentina; 53; 2; 11-2012; 13-23
0041-6932
1669-9637
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18935
identifier_str_mv Chiumiento, Eduardo Hernan; Examples of homogeneous manifolds with uniformly bounded metric projection; Unión Matemática Argentina; Revista de la Union Matemática Argentina; 53; 2; 11-2012; 13-23
0041-6932
1669-9637
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://inmabb.criba.edu.ar/revuma/pdf/v53n2/v53n2a02.pdf
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 Unión Matemática Argentina
publisher.none.fl_str_mv Unión Matemática Argentina
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15,812429

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