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.
Facultad de Ciencias Exactas - Materia
-
Matemática
Bessel sequence
Epimorphisms
Fibre bundle
Frame
Riesz sequence - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- http://creativecommons.org/licenses/by-nc-sa/4.0/
- Repositorio
.jpg)
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/83388
Ver los metadatos del registro completo
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Geometry of epimorphisms and framesCorach, GustavoPacheco, MiriamStojanoff, DemetrioMatemáticaBessel sequenceEpimorphismsFibre bundleFrameRiesz sequenceUsing 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.Facultad de Ciencias Exactas2004info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfhttp://sedici.unlp.edu.ar/handle/10915/83388enginfo:eu-repo/semantics/altIdentifier/issn/0002-9939info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-04-07380-0info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:07:43Zoai:sedici.unlp.edu.ar:10915/83388Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:07:43.375SEDICI (UNLP) - Universidad Nacional de La Platafalse |
| 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 Matemática Bessel sequence Epimorphisms Fibre bundle Frame 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 |
Matemática Bessel sequence Epimorphisms Fibre bundle Frame Riesz sequence |
| topic |
Matemática Bessel sequence Epimorphisms Fibre bundle Frame Riesz sequence |
| 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. Facultad de Ciencias Exactas |
| 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 |
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2004 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Articulo http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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http://sedici.unlp.edu.ar/handle/10915/83388 |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/issn/0002-9939 info:eu-repo/semantics/altIdentifier/doi/10.1090/S0002-9939-04-07380-0 |
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