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
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.
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Simon Bolivar.; Venezuela
Materia
DIFFERENCES OF PROJECTIONS
PAIRS OF PROJECTIONS
PROJECTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/106962
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Projections with fixed difference: a Hopf-Rinow theoremAndruchow, EstebanCorach, GustavoRecht, LázaroDIFFERENCES OF PROJECTIONSPAIRS OF PROJECTIONSPROJECTIONShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The 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.Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; ArgentinaFil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Simon Bolivar.; VenezuelaElsevier Science2019-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/106962Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; Projections with fixed difference: a Hopf-Rinow theorem; Elsevier Science; Differential Geometry and its Applications; 66; 10-2019; 155-1800926-2245CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.difgeo.2019.06.003info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1805.06856info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0926224518301554info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:54:04Zoai:ri.conicet.gov.ar:11336/106962instacron: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 09:54:04.673CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
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
DIFFERENCES OF PROJECTIONS
PAIRS OF PROJECTIONS
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 DIFFERENCES OF PROJECTIONS
PAIRS OF PROJECTIONS
PROJECTIONS
topic DIFFERENCES OF PROJECTIONS
PAIRS OF PROJECTIONS
PROJECTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Corach, Gustavo. Universidad de Buenos Aires. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Simon Bolivar.; Venezuela
description 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.
publishDate 2019
dc.date.none.fl_str_mv 2019-10
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/11336/106962
Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; Projections with fixed difference: a Hopf-Rinow theorem; Elsevier Science; Differential Geometry and its Applications; 66; 10-2019; 155-180
0926-2245
CONICET Digital
CONICET
url http://hdl.handle.net/11336/106962
identifier_str_mv Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; Projections with fixed difference: a Hopf-Rinow theorem; Elsevier Science; Differential Geometry and its Applications; 66; 10-2019; 155-180
0926-2245
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.difgeo.2019.06.003
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1805.06856
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0926224518301554
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
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 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 13.069144

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