Riemannian geometry of finite rank positive operators

Autores
Andruchow, Esteban; Varela, Alejandro
Año de publicación
2005
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
A riemannian metric is introduced in the infinite dimensional manifold Σ_n of positive operators with rank n<∞ on a Hilbert space H.  The geometry of this manifold is studied and related to the geometry of the submanifolds Σ_p$ of positive operators with range equal to the range of a projection p (rank of p =n), and P_p of selfadjoint projections in the connected component of p. It is shown that these spaces are complete in the geodesic distance.
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
POSITIVE OPERATOR
FINITE RANK PROJECTION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/104393
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Riemannian geometry of finite rank positive operatorsAndruchow, EstebanVarela, AlejandroPOSITIVE OPERATORFINITE RANK PROJECTIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1A riemannian metric is introduced in the infinite dimensional manifold Σ_n of positive operators with rank n<∞ on a Hilbert space H.  The geometry of this manifold is studied and related to the geometry of the submanifolds Σ_p$ of positive operators with range equal to the range of a projection p (rank of p =n), and P_p of selfadjoint projections in the connected component of p. It is shown that these spaces are complete in the geodesic distance.Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaElsevier Science2005-11info: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/11336/104393Andruchow, Esteban; Varela, Alejandro; Riemannian geometry of finite rank positive operators; Elsevier Science; Differential Geometry and its Applications; 23; 1; 11-2005; 305-3260926-2245CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.difgeo.2005.06.004info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0926224505000604info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:03:33Zoai:ri.conicet.gov.ar:11336/104393instacron: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:34982025-09-10 13:03:34.024CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Riemannian geometry of finite rank positive operators
title Riemannian geometry of finite rank positive operators
spellingShingle Riemannian geometry of finite rank positive operators
Andruchow, Esteban
POSITIVE OPERATOR
FINITE RANK PROJECTION
title_short Riemannian geometry of finite rank positive operators
title_full Riemannian geometry of finite rank positive operators
title_fullStr Riemannian geometry of finite rank positive operators
title_full_unstemmed Riemannian geometry of finite rank positive operators
title_sort Riemannian geometry of finite rank positive operators
dc.creator.none.fl_str_mv Andruchow, Esteban
Varela, Alejandro
author Andruchow, Esteban
author_facet Andruchow, Esteban
Varela, Alejandro
author_role author
author2 Varela, Alejandro
author2_role author
dc.subject.none.fl_str_mv POSITIVE OPERATOR
FINITE RANK PROJECTION
topic POSITIVE OPERATOR
FINITE RANK PROJECTION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv A riemannian metric is introduced in the infinite dimensional manifold Σ_n of positive operators with rank n<∞ on a Hilbert space H.  The geometry of this manifold is studied and related to the geometry of the submanifolds Σ_p$ of positive operators with range equal to the range of a projection p (rank of p =n), and P_p of selfadjoint projections in the connected component of p. It is shown that these spaces are complete in the geodesic distance.
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
description A riemannian metric is introduced in the infinite dimensional manifold Σ_n of positive operators with rank n<∞ on a Hilbert space H.  The geometry of this manifold is studied and related to the geometry of the submanifolds Σ_p$ of positive operators with range equal to the range of a projection p (rank of p =n), and P_p of selfadjoint projections in the connected component of p. It is shown that these spaces are complete in the geodesic distance.
publishDate 2005
dc.date.none.fl_str_mv 2005-11
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/11336/104393
Andruchow, Esteban; Varela, Alejandro; Riemannian geometry of finite rank positive operators; Elsevier Science; Differential Geometry and its Applications; 23; 1; 11-2005; 305-326
0926-2245
CONICET Digital
CONICET
url http://hdl.handle.net/11336/104393
identifier_str_mv Andruchow, Esteban; Varela, Alejandro; Riemannian geometry of finite rank positive operators; Elsevier Science; Differential Geometry and its Applications; 23; 1; 11-2005; 305-326
0926-2245
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.difgeo.2005.06.004
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0926224505000604
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier Science
publisher.none.fl_str_mv Elsevier Science
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 12.993085

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