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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/19424
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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 Técnicas2025-09-03T10:06:41Zoai: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:34982025-09-03 10:06:41.659CONICET 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 |
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13.13397 |