Essentially orthogonal subspaces

Autores
Andruchow, Esteban; Corach, Gustavo
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
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).
Fuente
Journal Of Operator Theory. Ene. 2018; 79(1): 79-100
https://www.theta.ro/jot/archive/2018-079-001/index_2018-079-001.html
Materia
Projections
Pairs of projections
Compact operators
Grasmann manifold
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/4.0/
Repositorio
Repositorio Institucional UNGS
Institución
Universidad Nacional de General Sarmiento
OAI Identificador
oai:repositorio.ungs.edu.ar:UNGS/1808
Acceder
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oai_identifier_str oai:repositorio.ungs.edu.ar:UNGS/1808
network_acronym_str RIUNGS
repository_id_str
network_name_str Repositorio Institucional UNGS
spelling Essentially orthogonal subspacesAndruchow, EstebanCorach, GustavoProjectionsPairs of projectionsCompact operatorsGrasmann manifoldFil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.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).Theta Foundation2024-12-23T13:21:48Z2024-12-23T13:21:48Z2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfAndruchow, E. y Corach, G. (2018). Essentially orthogonal subspaces. Journal Of Operator Theory, 79(1), 79-100.0379-4024http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1808Journal Of Operator Theory. Ene. 2018; 79(1): 79-100https://www.theta.ro/jot/archive/2018-079-001/index_2018-079-001.htmlreponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoeng10.7900/jot.2016dec13.2138info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2025-09-04T11:43:11Zoai:repositorio.ungs.edu.ar:UNGS/1808instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2025-09-04 11:43:11.409Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse
dc.title.none.fl_str_mv Essentially orthogonal subspaces
title Essentially orthogonal subspaces
spellingShingle Essentially orthogonal subspaces
Andruchow, Esteban
Projections
Pairs of projections
Compact operators
Grasmann 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
Pairs of projections
Compact operators
Grasmann manifold
topic Projections
Pairs of projections
Compact operators
Grasmann manifold
dc.description.none.fl_txt_mv Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
Fil: Corach, Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
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).
description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
publishDate 2018
dc.date.none.fl_str_mv 2018
2024-12-23T13:21:48Z
2024-12-23T13:21:48Z
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 Andruchow, E. y Corach, G. (2018). Essentially orthogonal subspaces. Journal Of Operator Theory, 79(1), 79-100.
0379-4024
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1808
identifier_str_mv Andruchow, E. y Corach, G. (2018). Essentially orthogonal subspaces. Journal Of Operator Theory, 79(1), 79-100.
0379-4024
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1808
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.7900/jot.2016dec13.2138
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.format.none.fl_str_mv 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 Journal Of Operator Theory. Ene. 2018; 79(1): 79-100
https://www.theta.ro/jot/archive/2018-079-001/index_2018-079-001.html
reponame:Repositorio Institucional UNGS
instname:Universidad Nacional de General Sarmiento
reponame_str Repositorio Institucional UNGS
collection Repositorio Institucional UNGS
instname_str Universidad Nacional de General Sarmiento
repository.name.fl_str_mv Repositorio Institucional UNGS - Universidad Nacional de General Sarmiento
repository.mail.fl_str_mv ubyd@campus.ungs.edu.ar
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score 12.623145

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