Geometry of epimorphisms and frames

Autores
Corach, Gustavo; Pacheco, Miriam; Stojanoff, Demetrio
Año de publicación
2004
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(ℓ2, H) of all (bounded linear) operators from ℓ2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F. We show that each component is a homogeneous space of the group GL(ℓ2) of invertible operators of ℓ2. This geometrical result shows that every smooth curve in F can be lifted to a curve in GL(ℓ2): given a smooth curve γ in F such that γ(0) = ξ, there exists a smooth curve γ in GL(ℓ2) such that γ = ξ, where the dot indicates the action of GL(ℓ2) over F. We also present a similar study of the set of Riesz sequences.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Pacheco, Miriam. No especifíca;
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
Materia
FIBRE BUNDLE
FRAME
EPIMORPHISMS
BESSEL SEQUENCE
RIESZ SEQUENCE
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:11336/109652
Acceder
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repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Geometry of epimorphisms and framesCorach, GustavoPacheco, MiriamStojanoff, DemetrioFIBRE BUNDLEFRAMEEPIMORPHISMSBESSEL SEQUENCERIESZ SEQUENCEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(ℓ2, H) of all (bounded linear) operators from ℓ2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F. We show that each component is a homogeneous space of the group GL(ℓ2) of invertible operators of ℓ2. This geometrical result shows that every smooth curve in F can be lifted to a curve in GL(ℓ2): given a smooth curve γ in F such that γ(0) = ξ, there exists a smooth curve γ in GL(ℓ2) such that γ = ξ, where the dot indicates the action of GL(ℓ2) over F. We also present a similar study of the set of Riesz sequences.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; ArgentinaFil: Pacheco, Miriam. No especifíca;Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; ArgentinaAmerican Mathematical Society2004-07info: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/11336/109652Corach, Gustavo; Pacheco, Miriam; Stojanoff, Demetrio; Geometry of epimorphisms and frames; American Mathematical Society; Proceedings of the American Mathematical Society; 132; 7; 7-2004; 2039-20490002-99391088-6826CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2004-132-07/home.htmlinfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2004-132-07/S0002-9939-04-07380-0/S0002-9939-04-07380-0.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 Técnicas2025-09-29T10:34:56Zoai:ri.conicet.gov.ar:11336/109652instacron: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 10:34:57.067CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Geometry of epimorphisms and frames
title Geometry of epimorphisms and frames
spellingShingle Geometry of epimorphisms and frames
Corach, Gustavo
FIBRE BUNDLE
FRAME
EPIMORPHISMS
BESSEL SEQUENCE
RIESZ SEQUENCE
title_short Geometry of epimorphisms and frames
title_full Geometry of epimorphisms and frames
title_fullStr Geometry of epimorphisms and frames
title_full_unstemmed Geometry of epimorphisms and frames
title_sort Geometry of epimorphisms and frames
dc.creator.none.fl_str_mv Corach, Gustavo
Pacheco, Miriam
Stojanoff, Demetrio
author Corach, Gustavo
author_facet Corach, Gustavo
Pacheco, Miriam
Stojanoff, Demetrio
author_role author
author2 Pacheco, Miriam
Stojanoff, Demetrio
author2_role author
author
dc.subject.none.fl_str_mv FIBRE BUNDLE
FRAME
EPIMORPHISMS
BESSEL SEQUENCE
RIESZ SEQUENCE
topic FIBRE BUNDLE
FRAME
EPIMORPHISMS
BESSEL SEQUENCE
RIESZ SEQUENCE
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(ℓ2, H) of all (bounded linear) operators from ℓ2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F. We show that each component is a homogeneous space of the group GL(ℓ2) of invertible operators of ℓ2. This geometrical result shows that every smooth curve in F can be lifted to a curve in GL(ℓ2): given a smooth curve γ in F such that γ(0) = ξ, there exists a smooth curve γ in GL(ℓ2) such that γ = ξ, where the dot indicates the action of GL(ℓ2) over F. We also present a similar study of the set of Riesz sequences.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina
Fil: Pacheco, Miriam. No especifíca;
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de La Plata; Argentina
description Using a bijection between the set BH of all Bessel sequences in a (separable) Hilbert space H and the space L(ℓ2, H) of all (bounded linear) operators from ℓ2 to H, we endow the set F of all frames in H with a natural topology for which we determine the connected components of F. We show that each component is a homogeneous space of the group GL(ℓ2) of invertible operators of ℓ2. This geometrical result shows that every smooth curve in F can be lifted to a curve in GL(ℓ2): given a smooth curve γ in F such that γ(0) = ξ, there exists a smooth curve γ in GL(ℓ2) such that γ = ξ, where the dot indicates the action of GL(ℓ2) over F. We also present a similar study of the set of Riesz sequences.
publishDate 2004
dc.date.none.fl_str_mv 2004-07
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/11336/109652
Corach, Gustavo; Pacheco, Miriam; Stojanoff, Demetrio; Geometry of epimorphisms and frames; American Mathematical Society; Proceedings of the American Mathematical Society; 132; 7; 7-2004; 2039-2049
0002-9939
1088-6826
CONICET Digital
CONICET
url http://hdl.handle.net/11336/109652
identifier_str_mv Corach, Gustavo; Pacheco, Miriam; Stojanoff, Demetrio; Geometry of epimorphisms and frames; American Mathematical Society; Proceedings of the American Mathematical Society; 132; 7; 7-2004; 2039-2049
0002-9939
1088-6826
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2004-132-07/home.html
info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/journals/proc/2004-132-07/S0002-9939-04-07380-0/S0002-9939-04-07380-0.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
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
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
_version_ 1844614366790418432
score 13.070432

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