Riemannian metrics on an infinite dimensional symplectic group

Autores
Lopez Galvan, Alberto Manuel
Año de publicación
2015
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The aim of this paper is the geometric study of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator. This subgroup of the symplectic group was introduced in Pierre de la Harpe´s classical book of Banach-Lie groups. Throughout this paper we will endow the tangent spaces with different Riemannian metrics. We will use the minimal curves of the unitary group and the positive invertible operators to compare the length of the geodesic curves in each case. Moreover we will study the completeness of the symplectic group with the geodesic distance.
Fil: Lopez Galvan, Alberto Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
Materia
Symplectic group
Riemann?Hilbert metric
Left-invariant metric
Complete metric space
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:11336/18949
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Riemannian metrics on an infinite dimensional symplectic groupLopez Galvan, Alberto ManuelSymplectic groupRiemann?Hilbert metricLeft-invariant metricComplete metric spacehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The aim of this paper is the geometric study of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator. This subgroup of the symplectic group was introduced in Pierre de la Harpe´s classical book of Banach-Lie groups. Throughout this paper we will endow the tangent spaces with different Riemannian metrics. We will use the minimal curves of the unitary group and the positive invertible operators to compare the length of the geodesic curves in each case. Moreover we will study the completeness of the symplectic group with the geodesic distance.Fil: Lopez Galvan, Alberto Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; ArgentinaElsevier2015-03info: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/11336/18949Lopez Galvan, Alberto Manuel; Riemannian metrics on an infinite dimensional symplectic group; Elsevier; Journal Of Mathematical Analysis And Applications; 428; 2; 3-2015; 1070-10840022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X15002760info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2015.03.051info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:45:54Zoai:ri.conicet.gov.ar:11336/18949instacron: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 10:45:55.01CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Riemannian metrics on an infinite dimensional symplectic group
title Riemannian metrics on an infinite dimensional symplectic group
spellingShingle Riemannian metrics on an infinite dimensional symplectic group
Lopez Galvan, Alberto Manuel
Symplectic group
Riemann?Hilbert metric
Left-invariant metric
Complete metric space
title_short Riemannian metrics on an infinite dimensional symplectic group
title_full Riemannian metrics on an infinite dimensional symplectic group
title_fullStr Riemannian metrics on an infinite dimensional symplectic group
title_full_unstemmed Riemannian metrics on an infinite dimensional symplectic group
title_sort Riemannian metrics on an infinite dimensional symplectic group
dc.creator.none.fl_str_mv Lopez Galvan, Alberto Manuel
author Lopez Galvan, Alberto Manuel
author_facet Lopez Galvan, Alberto Manuel
author_role author
dc.subject.none.fl_str_mv Symplectic group
Riemann?Hilbert metric
Left-invariant metric
Complete metric space
topic Symplectic group
Riemann?Hilbert metric
Left-invariant metric
Complete metric space
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 aim of this paper is the geometric study of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator. This subgroup of the symplectic group was introduced in Pierre de la Harpe´s classical book of Banach-Lie groups. Throughout this paper we will endow the tangent spaces with different Riemannian metrics. We will use the minimal curves of the unitary group and the positive invertible operators to compare the length of the geodesic curves in each case. Moreover we will study the completeness of the symplectic group with the geodesic distance.
Fil: Lopez Galvan, Alberto Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina
description The aim of this paper is the geometric study of the symplectic operators which are a perturbation of the identity by a Hilbert-Schmidt operator. This subgroup of the symplectic group was introduced in Pierre de la Harpe´s classical book of Banach-Lie groups. Throughout this paper we will endow the tangent spaces with different Riemannian metrics. We will use the minimal curves of the unitary group and the positive invertible operators to compare the length of the geodesic curves in each case. Moreover we will study the completeness of the symplectic group with the geodesic distance.
publishDate 2015
dc.date.none.fl_str_mv 2015-03
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/11336/18949
Lopez Galvan, Alberto Manuel; Riemannian metrics on an infinite dimensional symplectic group; Elsevier; Journal Of Mathematical Analysis And Applications; 428; 2; 3-2015; 1070-1084
0022-247X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/18949
identifier_str_mv Lopez Galvan, Alberto Manuel; Riemannian metrics on an infinite dimensional symplectic group; Elsevier; Journal Of Mathematical Analysis And Applications; 428; 2; 3-2015; 1070-1084
0022-247X
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://www.sciencedirect.com/science/article/pii/S0022247X15002760
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2015.03.051
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 Elsevier
publisher.none.fl_str_mv Elsevier
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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