Metric geometry of partial isometries in a finite von Neumann algebra
- Autores
- Andruchow, Esteban
- Año de publicación
- 2008
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- We study the geometry of the set Ip = v ∈ M: v∗v = p of partial isometries of a finite von Neumann algebra M, with initial space p (p is a projection of the algebra). This set is a C∞ submanifold of M in the norm topology of M. However, we study it in the strong operator topology, in which it does not have a smooth structure. This topology allows for the introduction of inner products on the tangent spaces by means of a fixed trace τ in M. The quadratic norms do not define a Hilbert–Riemann metric, for they are not complete. Nevertheless certain facts can be established: a restricted result on minimality of geodesics of the Levi-Civita connection, and uniqueness of these as the only possible minimal curves. We prove also that (Ip,dg) is a complete metric space, where dg is the geodesic distance of the manifold (or the metric given by the infima of lengths of piecewise smooth curves).
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 Calderon; Argentina - Materia
-
Partial Isometry
Finite Algebra
Homogeneous Spaces - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/19448
Ver los metadatos del registro completo
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Metric geometry of partial isometries in a finite von Neumann algebraAndruchow, EstebanPartial IsometryFinite AlgebraHomogeneous Spaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the geometry of the set Ip = v ∈ M: v∗v = p of partial isometries of a finite von Neumann algebra M, with initial space p (p is a projection of the algebra). This set is a C∞ submanifold of M in the norm topology of M. However, we study it in the strong operator topology, in which it does not have a smooth structure. This topology allows for the introduction of inner products on the tangent spaces by means of a fixed trace τ in M. The quadratic norms do not define a Hilbert–Riemann metric, for they are not complete. Nevertheless certain facts can be established: a restricted result on minimality of geodesics of the Levi-Civita connection, and uniqueness of these as the only possible minimal curves. We prove also that (Ip,dg) is a complete metric space, where dg is the geodesic distance of the manifold (or the metric given by the infima of lengths of piecewise smooth curves).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 Calderon; ArgentinaElsevier2008-12info: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/11336/19448Andruchow, Esteban; Metric geometry of partial isometries in a finite von Neumann algebra; Elsevier; Journal Of Mathematical Analysis And Applications; 337; 2; 12-2008; 1226-12370022-247XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X07005124info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2007.04.056info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:47:36Zoai:ri.conicet.gov.ar:11336/19448instacron: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 10:47:36.571CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
dc.title.none.fl_str_mv |
Metric geometry of partial isometries in a finite von Neumann algebra |
title |
Metric geometry of partial isometries in a finite von Neumann algebra |
spellingShingle |
Metric geometry of partial isometries in a finite von Neumann algebra Andruchow, Esteban Partial Isometry Finite Algebra Homogeneous Spaces |
title_short |
Metric geometry of partial isometries in a finite von Neumann algebra |
title_full |
Metric geometry of partial isometries in a finite von Neumann algebra |
title_fullStr |
Metric geometry of partial isometries in a finite von Neumann algebra |
title_full_unstemmed |
Metric geometry of partial isometries in a finite von Neumann algebra |
title_sort |
Metric geometry of partial isometries in a finite von Neumann algebra |
dc.creator.none.fl_str_mv |
Andruchow, Esteban |
author |
Andruchow, Esteban |
author_facet |
Andruchow, Esteban |
author_role |
author |
dc.subject.none.fl_str_mv |
Partial Isometry Finite Algebra Homogeneous Spaces |
topic |
Partial Isometry Finite Algebra Homogeneous Spaces |
purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
dc.description.none.fl_txt_mv |
We study the geometry of the set Ip = v ∈ M: v∗v = p of partial isometries of a finite von Neumann algebra M, with initial space p (p is a projection of the algebra). This set is a C∞ submanifold of M in the norm topology of M. However, we study it in the strong operator topology, in which it does not have a smooth structure. This topology allows for the introduction of inner products on the tangent spaces by means of a fixed trace τ in M. The quadratic norms do not define a Hilbert–Riemann metric, for they are not complete. Nevertheless certain facts can be established: a restricted result on minimality of geodesics of the Levi-Civita connection, and uniqueness of these as the only possible minimal curves. We prove also that (Ip,dg) is a complete metric space, where dg is the geodesic distance of the manifold (or the metric given by the infima of lengths of piecewise smooth curves). 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 Calderon; Argentina |
description |
We study the geometry of the set Ip = v ∈ M: v∗v = p of partial isometries of a finite von Neumann algebra M, with initial space p (p is a projection of the algebra). This set is a C∞ submanifold of M in the norm topology of M. However, we study it in the strong operator topology, in which it does not have a smooth structure. This topology allows for the introduction of inner products on the tangent spaces by means of a fixed trace τ in M. The quadratic norms do not define a Hilbert–Riemann metric, for they are not complete. Nevertheless certain facts can be established: a restricted result on minimality of geodesics of the Levi-Civita connection, and uniqueness of these as the only possible minimal curves. We prove also that (Ip,dg) is a complete metric space, where dg is the geodesic distance of the manifold (or the metric given by the infima of lengths of piecewise smooth curves). |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008-12 |
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/11336/19448 Andruchow, Esteban; Metric geometry of partial isometries in a finite von Neumann algebra; Elsevier; Journal Of Mathematical Analysis And Applications; 337; 2; 12-2008; 1226-1237 0022-247X CONICET Digital CONICET |
url |
http://hdl.handle.net/11336/19448 |
identifier_str_mv |
Andruchow, Esteban; Metric geometry of partial isometries in a finite von Neumann algebra; Elsevier; Journal Of Mathematical Analysis And Applications; 337; 2; 12-2008; 1226-1237 0022-247X CONICET Digital CONICET |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022247X07005124 info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jmaa.2007.04.056 |
dc.rights.none.fl_str_mv |
info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
eu_rights_str_mv |
openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
dc.format.none.fl_str_mv |
application/pdf application/pdf application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
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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1844614520557797376 |
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13.070432 |