Geometry of epimorphisms and frames

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 c...

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Detalles Bibliográficos
Autores principales: Corach, Gustavo, Pacheco, Miriam, Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2004
Materias:
Matemática
Bessel sequence
Epimorphisms
Fibre bundle
Frame
Riesz sequence
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/83388
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-83388
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Bessel sequence
Epimorphisms
Fibre bundle
Frame
Riesz sequence
spellingShingle Matemática
Bessel sequence
Epimorphisms
Fibre bundle
Frame
Riesz sequence
Corach, Gustavo
Pacheco, Miriam
Stojanoff, Demetrio
Geometry of epimorphisms and frames
topic_facet Matemática
Bessel sequence
Epimorphisms
Fibre bundle
Frame
Riesz sequence
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.
format Articulo
Articulo
author Corach, Gustavo
Pacheco, Miriam
Stojanoff, Demetrio
author_facet Corach, Gustavo
Pacheco, Miriam
Stojanoff, Demetrio
author_sort Corach, Gustavo
title Geometry of epimorphisms and frames
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
publishDate 2004
url http://sedici.unlp.edu.ar/handle/10915/83388
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AT pachecomiriam geometryofepimorphismsandframes
AT stojanoffdemetrio geometryofepimorphismsandframes
bdutipo_str Repositorios
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