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
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/88438
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/88438
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling 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 Técnicas2025-10-15T14:43:23Zoai: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:34982025-10-15 14:43:23.767CONICET 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
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 13.22299

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