Some properties of frames of subspaces obtained by operator theory methods

We study the relationship among operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E = {Ei}i ∈ I of a Hilbert space K and a surjective T ∈ L (K, H) in order t...

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Detalles Bibliográficos
Autores principales: Ruiz, Mariano Andrés, Stojanoff, Demetrio
Formato: Articulo
Lenguaje:Inglés
Publicado: 2008
Materias:
Matemática
Frames
Frames of subspaces
Fusion frames
Hilbert space operators
Oblique projections
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/84315
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-84315
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Frames
Frames of subspaces
Fusion frames
Hilbert space operators
Oblique projections
spellingShingle Matemática
Frames
Frames of subspaces
Fusion frames
Hilbert space operators
Oblique projections
Ruiz, Mariano Andrés
Stojanoff, Demetrio
Some properties of frames of subspaces obtained by operator theory methods
topic_facet Matemática
Frames
Frames of subspaces
Fusion frames
Hilbert space operators
Oblique projections
description We study the relationship among operators, orthonormal basis of subspaces and frames of subspaces (also called fusion frames) for a separable Hilbert space H. We get sufficient conditions on an orthonormal basis of subspaces E = {Ei}i ∈ I of a Hilbert space K and a surjective T ∈ L (K, H) in order that {T (Ei)}i ∈ I is a frame of subspaces with respect to a computable sequence of weights. We also obtain generalizations of results in [J.A. Antezana, G. Corach, M. Ruiz, D. Stojanoff, Oblique projections and frames, Proc. Amer. Math. Soc. 134 (2006) 1031-1037], which relate frames of subspaces (including the computation of their weights) and oblique projections. The notion of refinement of a fusion frame is defined and used to obtain results about the excess of such frames. We study the set of admissible weights for a generating sequence of subspaces. Several examples are given.
format Articulo
Articulo
author Ruiz, Mariano Andrés
Stojanoff, Demetrio
author_facet Ruiz, Mariano Andrés
Stojanoff, Demetrio
author_sort Ruiz, Mariano Andrés
title Some properties of frames of subspaces obtained by operator theory methods
title_short Some properties of frames of subspaces obtained by operator theory methods
title_full Some properties of frames of subspaces obtained by operator theory methods
title_fullStr Some properties of frames of subspaces obtained by operator theory methods
title_full_unstemmed Some properties of frames of subspaces obtained by operator theory methods
title_sort some properties of frames of subspaces obtained by operator theory methods
publishDate 2008
url http://sedici.unlp.edu.ar/handle/10915/84315
work_keys_str_mv AT ruizmarianoandres somepropertiesofframesofsubspacesobtainedbyoperatortheorymethods
AT stojanoffdemetrio somepropertiesofframesofsubspacesobtainedbyoperatortheorymethods
bdutipo_str Repositorios
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