The Grassmann manifold of a Hilbert space

Autores
Andruchow, Esteban
Año de publicación
2014
Idioma
inglés
Tipo de recurso
documento de conferencia
Estado
versión publicada
Descripción
The present paper surveys the geometric properties of the Grassmann manifold Gr(H ) of an infinite dimensional complex Hilbert space H . Gr(H ) is viewed as a set of operators, identifying each closed subspace S ⊂ H with the orthogonal projection PS onto S . Most of the results surveyed here were stated by G. Corach, H. Porta and L. Recht: submanifold structure, homogeneous reductive structure, local minimality of geodesics. Some recent results concerning the existence and uniqueness of a geodesic joining two given projections, which were obtained by the present author, are also presented.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
XII Congreso Antonio Monteiro
Bahía Blanca
Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca
Materia
Subspaces of a Hilbert space
Projections
Geodesics
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:11336/159858
Acceder
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network_name_str CONICET Digital (CONICET)
spelling The Grassmann manifold of a Hilbert spaceAndruchow, EstebanSubspaces of a Hilbert spaceProjectionsGeodesicshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The present paper surveys the geometric properties of the Grassmann manifold Gr(H ) of an infinite dimensional complex Hilbert space H . Gr(H ) is viewed as a set of operators, identifying each closed subspace S ⊂ H with the orthogonal projection PS onto S . Most of the results surveyed here were stated by G. Corach, H. Porta and L. Recht: submanifold structure, homogeneous reductive structure, local minimality of geodesics. Some recent results concerning the existence and uniqueness of a geodesic joining two given projections, which were obtained by the present author, are also presented.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaXII Congreso Antonio MonteiroBahía BlancaArgentinaConsejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía BlancaConsejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca2014info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjectCongresoJournalhttp://purl.org/coar/resource_type/c_5794info:ar-repo/semantics/documentoDeConferenciaapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/159858The Grassmann manifold of a Hilbert space; XII Congreso Antonio Monteiro; Bahía Blanca; Argentina; 2013; 41-55CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://inmabb.conicet.gob.ar/static/publicaciones/actas/12/08-andruchow.pdfinfo:eu-repo/semantics/altIdentifier/url/http://inmabb.conicet.gob.ar/publicaciones/actas-del-congreso-monteiro/12Internacionalinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:05:22Zoai:ri.conicet.gov.ar:11336/159858instacron: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:34982025-09-29 10:05:23.02CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv The Grassmann manifold of a Hilbert space
title The Grassmann manifold of a Hilbert space
spellingShingle The Grassmann manifold of a Hilbert space
Andruchow, Esteban
Subspaces of a Hilbert space
Projections
Geodesics
title_short The Grassmann manifold of a Hilbert space
title_full The Grassmann manifold of a Hilbert space
title_fullStr The Grassmann manifold of a Hilbert space
title_full_unstemmed The Grassmann manifold of a Hilbert space
title_sort The Grassmann manifold of a Hilbert space
dc.creator.none.fl_str_mv Andruchow, Esteban
author Andruchow, Esteban
author_facet Andruchow, Esteban
author_role author
dc.subject.none.fl_str_mv Subspaces of a Hilbert space
Projections
Geodesics
topic Subspaces of a Hilbert space
Projections
Geodesics
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The present paper surveys the geometric properties of the Grassmann manifold Gr(H ) of an infinite dimensional complex Hilbert space H . Gr(H ) is viewed as a set of operators, identifying each closed subspace S ⊂ H with the orthogonal projection PS onto S . Most of the results surveyed here were stated by G. Corach, H. Porta and L. Recht: submanifold structure, homogeneous reductive structure, local minimality of geodesics. Some recent results concerning the existence and uniqueness of a geodesic joining two given projections, which were obtained by the present author, are also presented.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
XII Congreso Antonio Monteiro
Bahía Blanca
Argentina
Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca
description The present paper surveys the geometric properties of the Grassmann manifold Gr(H ) of an infinite dimensional complex Hilbert space H . Gr(H ) is viewed as a set of operators, identifying each closed subspace S ⊂ H with the orthogonal projection PS onto S . Most of the results surveyed here were stated by G. Corach, H. Porta and L. Recht: submanifold structure, homogeneous reductive structure, local minimality of geodesics. Some recent results concerning the existence and uniqueness of a geodesic joining two given projections, which were obtained by the present author, are also presented.
publishDate 2014
dc.date.none.fl_str_mv 2014
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
Congreso
Journal
http://purl.org/coar/resource_type/c_5794
info:ar-repo/semantics/documentoDeConferencia
status_str publishedVersion
format conferenceObject
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/159858
The Grassmann manifold of a Hilbert space; XII Congreso Antonio Monteiro; Bahía Blanca; Argentina; 2013; 41-55
CONICET Digital
CONICET
url http://hdl.handle.net/11336/159858
identifier_str_mv The Grassmann manifold of a Hilbert space; XII Congreso Antonio Monteiro; Bahía Blanca; Argentina; 2013; 41-55
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.conicet.gob.ar/static/publicaciones/actas/12/08-andruchow.pdf
info:eu-repo/semantics/altIdentifier/url/http://inmabb.conicet.gob.ar/publicaciones/actas-del-congreso-monteiro/12
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.coverage.none.fl_str_mv Internacional
dc.publisher.none.fl_str_mv Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca
publisher.none.fl_str_mv Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca
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 13.070432

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