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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/106962
Ver los metadatos del registro completo
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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 Técnicas2025-09-03T09:53:56Zoai: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:34982025-09-03 09:53:56.599CONICET 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/ |
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openAccess |
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https://creativecommons.org/licenses/by-nc-nd/2.5/ar/ |
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application/pdf application/pdf application/pdf |
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Elsevier Science |
publisher.none.fl_str_mv |
Elsevier Science |
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reponame:CONICET Digital (CONICET) instname:Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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