Some properties of frames of subspaces obtained by operator theory methods

Autores
Ruiz, Mariano Andres; Stojanoff, Demetrio
Año de publicación
2008
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Materia
FRAMES
FRAMES OF SUBSPACES
FUSION FRAMES
HILBERT SPACE OPERATORS
OBLIQUE PROJECTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/93026
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/93026
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Some properties of frames of subspaces obtained by operator theory methodsRuiz, Mariano AndresStojanoff, DemetrioFRAMESFRAMES OF SUBSPACESFUSION FRAMESHILBERT SPACE OPERATORSOBLIQUE PROJECTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We 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.Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaAcademic Press Inc Elsevier Science2008-07-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/93026Ruiz, Mariano Andres; Stojanoff, Demetrio; Some properties of frames of subspaces obtained by operator theory methods; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 343; 1; 1-7-2008; 366-3780022-247X1096-0813CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2008.01.062info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X08000826info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-26T08:39:48Zoai:ri.conicet.gov.ar:11336/93026instacron: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:34982025-11-26 08:39:48.295CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Some properties of frames of subspaces obtained by operator theory methods
title Some properties of frames of subspaces obtained by operator theory methods
spellingShingle Some properties of frames of subspaces obtained by operator theory methods
Ruiz, Mariano Andres
FRAMES
FRAMES OF SUBSPACES
FUSION FRAMES
HILBERT SPACE OPERATORS
OBLIQUE PROJECTIONS
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
dc.creator.none.fl_str_mv Ruiz, Mariano Andres
Stojanoff, Demetrio
author Ruiz, Mariano Andres
author_facet Ruiz, Mariano Andres
Stojanoff, Demetrio
author_role author
author2 Stojanoff, Demetrio
author2_role author
dc.subject.none.fl_str_mv FRAMES
FRAMES OF SUBSPACES
FUSION FRAMES
HILBERT SPACE OPERATORS
OBLIQUE PROJECTIONS
topic FRAMES
FRAMES OF SUBSPACES
FUSION FRAMES
HILBERT SPACE OPERATORS
OBLIQUE PROJECTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Ruiz, Mariano Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Stojanoff, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
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.
publishDate 2008
dc.date.none.fl_str_mv 2008-07-01
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/11336/93026
Ruiz, Mariano Andres; Stojanoff, Demetrio; Some properties of frames of subspaces obtained by operator theory methods; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 343; 1; 1-7-2008; 366-378
0022-247X
1096-0813
CONICET Digital
CONICET
url http://hdl.handle.net/11336/93026
identifier_str_mv Ruiz, Mariano Andres; Stojanoff, Demetrio; Some properties of frames of subspaces obtained by operator theory methods; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 343; 1; 1-7-2008; 366-378
0022-247X
1096-0813
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2008.01.062
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022247X08000826
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Inc Elsevier Science
publisher.none.fl_str_mv Academic Press Inc Elsevier Science
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 13.011256

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