Redundant decompositions, angles between subspaces and oblique projections

Autores
Corach, Gustavo; Maestripieri, Alejandra Laura
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Let H be a complex Hilbert space. We study the relationships between the angles between closed subspaces of H, the oblique projections associated to non direct decompositions of H and a notion of compatibility between a positive (semidefinite) operator A acting on H and a closed subspace S of H. It turns out that the compatibility is ruled by the values of the Dixmier angle between the orthogonal complement S⊥ of S and the closure of AS. We show that every redundant decomposition H = S+M⊥ (where redundant means that S ∩M⊥ is not trivial) occurs in the presence of a certain compatibility. We also show applications of these results to some signal processing problems (consistent reconstruction) and to abstract splines problems which come from approximation theory.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina
Materia
OBLIQUE PROJECTIONS
ANGLE BETWEEN SUBSPACES
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:11336/19424
Acceder
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spelling Redundant decompositions, angles between subspaces and oblique projectionsCorach, GustavoMaestripieri, Alejandra LauraOBLIQUE PROJECTIONSANGLE BETWEEN SUBSPACEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let H be a complex Hilbert space. We study the relationships between the angles between closed subspaces of H, the oblique projections associated to non direct decompositions of H and a notion of compatibility between a positive (semidefinite) operator A acting on H and a closed subspace S of H. It turns out that the compatibility is ruled by the values of the Dixmier angle between the orthogonal complement S⊥ of S and the closure of AS. We show that every redundant decomposition H = S+M⊥ (where redundant means that S ∩M⊥ is not trivial) occurs in the presence of a certain compatibility. We also show applications of these results to some signal processing problems (consistent reconstruction) and to abstract splines problems which come from approximation theory.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; ArgentinaFil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; ArgentinaUniv Autonoma Barcelona2010-03info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/19424Corach, Gustavo; Maestripieri, Alejandra Laura; Redundant decompositions, angles between subspaces and oblique projections; Univ Autonoma Barcelona; Publicacions Matematiques; 54; 2; 3-2010; 461-4840214-1493CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://mat.uab.es/pubmat/volums/navegador#info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-11-05T10:36:11Zoai:ri.conicet.gov.ar:11336/19424instacron: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:34982025-11-05 10:36:11.796CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Redundant decompositions, angles between subspaces and oblique projections
title Redundant decompositions, angles between subspaces and oblique projections
spellingShingle Redundant decompositions, angles between subspaces and oblique projections
Corach, Gustavo
OBLIQUE PROJECTIONS
ANGLE BETWEEN SUBSPACES
title_short Redundant decompositions, angles between subspaces and oblique projections
title_full Redundant decompositions, angles between subspaces and oblique projections
title_fullStr Redundant decompositions, angles between subspaces and oblique projections
title_full_unstemmed Redundant decompositions, angles between subspaces and oblique projections
title_sort Redundant decompositions, angles between subspaces and oblique projections
dc.creator.none.fl_str_mv Corach, Gustavo
Maestripieri, Alejandra Laura
author Corach, Gustavo
author_facet Corach, Gustavo
Maestripieri, Alejandra Laura
author_role author
author2 Maestripieri, Alejandra Laura
author2_role author
dc.subject.none.fl_str_mv OBLIQUE PROJECTIONS
ANGLE BETWEEN SUBSPACES
topic OBLIQUE PROJECTIONS
ANGLE BETWEEN SUBSPACES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv Let H be a complex Hilbert space. We study the relationships between the angles between closed subspaces of H, the oblique projections associated to non direct decompositions of H and a notion of compatibility between a positive (semidefinite) operator A acting on H and a closed subspace S of H. It turns out that the compatibility is ruled by the values of the Dixmier angle between the orthogonal complement S⊥ of S and the closure of AS. We show that every redundant decomposition H = S+M⊥ (where redundant means that S ∩M⊥ is not trivial) occurs in the presence of a certain compatibility. We also show applications of these results to some signal processing problems (consistent reconstruction) and to abstract splines problems which come from approximation theory.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina
Fil: Maestripieri, Alejandra Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad de Buenos Aires. Facultad de Ingeniería. Departamento de Matemáticas; Argentina
description Let H be a complex Hilbert space. We study the relationships between the angles between closed subspaces of H, the oblique projections associated to non direct decompositions of H and a notion of compatibility between a positive (semidefinite) operator A acting on H and a closed subspace S of H. It turns out that the compatibility is ruled by the values of the Dixmier angle between the orthogonal complement S⊥ of S and the closure of AS. We show that every redundant decomposition H = S+M⊥ (where redundant means that S ∩M⊥ is not trivial) occurs in the presence of a certain compatibility. We also show applications of these results to some signal processing problems (consistent reconstruction) and to abstract splines problems which come from approximation theory.
publishDate 2010
dc.date.none.fl_str_mv 2010-03
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/11336/19424
Corach, Gustavo; Maestripieri, Alejandra Laura; Redundant decompositions, angles between subspaces and oblique projections; Univ Autonoma Barcelona; Publicacions Matematiques; 54; 2; 3-2010; 461-484
0214-1493
CONICET Digital
CONICET
url http://hdl.handle.net/11336/19424
identifier_str_mv Corach, Gustavo; Maestripieri, Alejandra Laura; Redundant decompositions, angles between subspaces and oblique projections; Univ Autonoma Barcelona; Publicacions Matematiques; 54; 2; 3-2010; 461-484
0214-1493
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://mat.uab.es/pubmat/volums/navegador#
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
dc.publisher.none.fl_str_mv Univ Autonoma Barcelona
publisher.none.fl_str_mv Univ Autonoma Barcelona
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_ 1847978050404220928
score 13.087074

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