Essentially orthogonal subspaces
- Autores
- Andruchow, Esteban; Corach, Gustavo
- Año de publicación
- 2018
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We study the set C consisting of pairs of orthogonal projectionsP,Q acting in a Hilbert space H such that PQ is a compact operator. Thesepairs have a rich geometric structure which we describe here. They are partitionedin three subclasses: C0 consists of pairs where P or Q have finite rank,C1 of pairs such that Q lies in the restricted Grassmannian (also called Sato-Grassmannian) of the polarization H = N(P)⊕ R(P), and C∞. We characterize the connected components of these classes: the components of C0 are parametrized by the rank, the components of C1 are parametrized by the Fredholm index of the pairs, and C∞ is connected. We show that these subsets are(non-complemented) differentiable submanifolds of B(H) x B(H).
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina - Materia
-
PROJECTIONS
PAIR OF PROJECTIONS
COMPACT OPERATORS
GRASSMANN MANIFOLD - 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:11336/88438
Ver los metadatos del registro completo
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Essentially orthogonal subspacesAndruchow, EstebanCorach, GustavoPROJECTIONSPAIR OF PROJECTIONSCOMPACT OPERATORSGRASSMANN MANIFOLDhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the set C consisting of pairs of orthogonal projectionsP,Q acting in a Hilbert space H such that PQ is a compact operator. Thesepairs have a rich geometric structure which we describe here. They are partitionedin three subclasses: C0 consists of pairs where P or Q have finite rank,C1 of pairs such that Q lies in the restricted Grassmannian (also called Sato-Grassmannian) of the polarization H = N(P)⊕ R(P), and C∞. We characterize the connected components of these classes: the components of C0 are parametrized by the rank, the components of C1 are parametrized by the Fredholm index of the pairs, and C∞ is connected. We show that these subsets are(non-complemented) differentiable submanifolds of B(H) x B(H).Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaTheta Foundation2018-01info: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/11336/88438Andruchow, Esteban; Corach, Gustavo; Essentially orthogonal subspaces; Theta Foundation; Journal Of Operator Theory; 79; 1; 1-2018; 79-1000379-4024CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.theta.ro/jot/archive/2018-079-001/index_2018-079-001.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:49:20Zoai:ri.conicet.gov.ar:11336/88438instacron: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:34982025-09-29 09:49:20.596CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Essentially orthogonal subspaces |
title |
Essentially orthogonal subspaces |
spellingShingle |
Essentially orthogonal subspaces Andruchow, Esteban PROJECTIONS PAIR OF PROJECTIONS COMPACT OPERATORS GRASSMANN MANIFOLD |
title_short |
Essentially orthogonal subspaces |
title_full |
Essentially orthogonal subspaces |
title_fullStr |
Essentially orthogonal subspaces |
title_full_unstemmed |
Essentially orthogonal subspaces |
title_sort |
Essentially orthogonal subspaces |
dc.creator.none.fl_str_mv |
Andruchow, Esteban Corach, Gustavo |
author |
Andruchow, Esteban |
author_facet |
Andruchow, Esteban Corach, Gustavo |
author_role |
author |
author2 |
Corach, Gustavo |
author2_role |
author |
dc.subject.none.fl_str_mv |
PROJECTIONS PAIR OF PROJECTIONS COMPACT OPERATORS GRASSMANN MANIFOLD |
topic |
PROJECTIONS PAIR OF PROJECTIONS COMPACT OPERATORS GRASSMANN MANIFOLD |
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 set C consisting of pairs of orthogonal projectionsP,Q acting in a Hilbert space H such that PQ is a compact operator. Thesepairs have a rich geometric structure which we describe here. They are partitionedin three subclasses: C0 consists of pairs where P or Q have finite rank,C1 of pairs such that Q lies in the restricted Grassmannian (also called Sato-Grassmannian) of the polarization H = N(P)⊕ R(P), and C∞. We characterize the connected components of these classes: the components of C0 are parametrized by the rank, the components of C1 are parametrized by the Fredholm index of the pairs, and C∞ is connected. We show that these subsets are(non-complemented) differentiable submanifolds of B(H) x B(H). Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina |
description |
We study the set C consisting of pairs of orthogonal projectionsP,Q acting in a Hilbert space H such that PQ is a compact operator. Thesepairs have a rich geometric structure which we describe here. They are partitionedin three subclasses: C0 consists of pairs where P or Q have finite rank,C1 of pairs such that Q lies in the restricted Grassmannian (also called Sato-Grassmannian) of the polarization H = N(P)⊕ R(P), and C∞. We characterize the connected components of these classes: the components of C0 are parametrized by the rank, the components of C1 are parametrized by the Fredholm index of the pairs, and C∞ is connected. We show that these subsets are(non-complemented) differentiable submanifolds of B(H) x B(H). |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-01 |
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/11336/88438 Andruchow, Esteban; Corach, Gustavo; Essentially orthogonal subspaces; Theta Foundation; Journal Of Operator Theory; 79; 1; 1-2018; 79-100 0379-4024 CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/88438 |
identifier_str_mv |
Andruchow, Esteban; Corach, Gustavo; Essentially orthogonal subspaces; Theta Foundation; Journal Of Operator Theory; 79; 1; 1-2018; 79-100 0379-4024 CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/https://www.theta.ro/jot/archive/2018-079-001/index_2018-079-001.html |
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 application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Theta Foundation |
publisher.none.fl_str_mv |
Theta Foundation |
dc.source.none.fl_str_mv |
reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
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CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas |
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dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar |
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