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
- Institución
- Universidad Nacional de General Sarmiento
- OAI Identificador
- oai:repositorio.ungs.edu.ar:UNGS/1804
Ver los metadatos del registro completo
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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/4.0/2025-09-04T11:43:15Zoai: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:2025-09-04 11:43:15.743Repositorio 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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1842346540656492544 |
score |
12.623145 |