Projections with fixed difference : a Hopf-Rinow theorem

Autores
Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro
Año de publicación
2019
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.
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
The set D_A0 , of pairs of orthogonal projections (P,Q) in generic position with fixed difference P?Q=A_0, is shown to be a homogeneous smooth manifold: it is the quotient of the unitary group of the commutant {A_0}' divided by the unitary subgroup of the commutant {P0,Q0}', where (P0,Q0) is any fixed pair in D_A0. Endowed with a natural reductive structure (a linear connection) and the quotient Finsler metric of the operator norm, it behaves as a classic Riemannian space: any two pairs in D_A0 are joined by a geodesic of minimal length. Given a base pair (P0,Q0), pairs in an open dense subset of DA0 can be joined to (P0,Q0) by a unique minimal geodesic.
Fuente
Differential Geometry and its Applications. 2019; 66: 155-180
https://www.sciencedirect.com/journal/differential-geometry-and-its-applications/vol/66/suppl/C
Materia
Projections
Pairs of projections
Differences of projections
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/1804
Acceder
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oai_identifier_str oai:repositorio.ungs.edu.ar:UNGS/1804
network_acronym_str RIUNGS
repository_id_str
network_name_str Repositorio Institucional UNGS
spelling Projections with fixed difference : a Hopf-Rinow theoremAndruchow, EstebanCorach, GustavoRecht, LázaroProjectionsPairs of projectionsDifferences of projectionsFil: 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.Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.The set D_A0 , of pairs of orthogonal projections (P,Q) in generic position with fixed difference P?Q=A_0, is shown to be a homogeneous smooth manifold: it is the quotient of the unitary group of the commutant {A_0}' divided by the unitary subgroup of the commutant {P0,Q0}', where (P0,Q0) is any fixed pair in D_A0. Endowed with a natural reductive structure (a linear connection) and the quotient Finsler metric of the operator norm, it behaves as a classic Riemannian space: any two pairs in D_A0 are joined by a geodesic of minimal length. Given a base pair (P0,Q0), pairs in an open dense subset of DA0 can be joined to (P0,Q0) by a unique minimal geodesic.Elsevier Science2024-12-23T13:21:47Z2024-12-23T13:21:47Z2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfAndruchow, E., Corach, G. y Recht, L. (2019). Projections with fixed difference: a Hopf-Rinow theorem. Differential Geometry and its Applications, 66, 155-180.0926-2245http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1804Differential Geometry and its Applications. 2019; 66: 155-180https://www.sciencedirect.com/journal/differential-geometry-and-its-applications/vol/66/suppl/Creponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoenghttp://dx.doi.org/10.1016/j.difgeo.2019.06.003info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2025-10-16T15:29:29Zoai:repositorio.ungs.edu.ar:UNGS/1804instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2025-10-16 15:29:30.236Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse
dc.title.none.fl_str_mv Projections with fixed difference : a Hopf-Rinow theorem
title Projections with fixed difference : a Hopf-Rinow theorem
spellingShingle Projections with fixed difference : a Hopf-Rinow theorem
Andruchow, Esteban
Projections
Pairs of projections
Differences of projections
title_short Projections with fixed difference : a Hopf-Rinow theorem
title_full Projections with fixed difference : a Hopf-Rinow theorem
title_fullStr Projections with fixed difference : a Hopf-Rinow theorem
title_full_unstemmed Projections with fixed difference : a Hopf-Rinow theorem
title_sort Projections with fixed difference : a Hopf-Rinow theorem
dc.creator.none.fl_str_mv Andruchow, Esteban
Corach, Gustavo
Recht, Lázaro
author Andruchow, Esteban
author_facet Andruchow, Esteban
Corach, Gustavo
Recht, Lázaro
author_role author
author2 Corach, Gustavo
Recht, Lázaro
author2_role author
author
dc.subject.none.fl_str_mv Projections
Pairs of projections
Differences of projections
topic Projections
Pairs of projections
Differences of projections
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.
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto Argentino de Matemática "Alberto P. Calderón"; Argentina.
The set D_A0 , of pairs of orthogonal projections (P,Q) in generic position with fixed difference P?Q=A_0, is shown to be a homogeneous smooth manifold: it is the quotient of the unitary group of the commutant {A_0}' divided by the unitary subgroup of the commutant {P0,Q0}', where (P0,Q0) is any fixed pair in D_A0. Endowed with a natural reductive structure (a linear connection) and the quotient Finsler metric of the operator norm, it behaves as a classic Riemannian space: any two pairs in D_A0 are joined by a geodesic of minimal length. Given a base pair (P0,Q0), pairs in an open dense subset of DA0 can be joined to (P0,Q0) by a unique minimal geodesic.
description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
publishDate 2019
dc.date.none.fl_str_mv 2019
2024-12-23T13:21:47Z
2024-12-23T13:21:47Z
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., Corach, G. y Recht, L. (2019). Projections with fixed difference: a Hopf-Rinow theorem. Differential Geometry and its Applications, 66, 155-180.
0926-2245
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1804
identifier_str_mv Andruchow, E., Corach, G. y Recht, L. (2019). Projections with fixed difference: a Hopf-Rinow theorem. Differential Geometry and its Applications, 66, 155-180.
0926-2245
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1804
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv http://dx.doi.org/10.1016/j.difgeo.2019.06.003
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 Elsevier Science
publisher.none.fl_str_mv Elsevier Science
dc.source.none.fl_str_mv Differential Geometry and its Applications. 2019; 66: 155-180
https://www.sciencedirect.com/journal/differential-geometry-and-its-applications/vol/66/suppl/C
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 12.375692

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