States with equivalent supports
- Autores
- Andruchow, Esteban; Varela, Alejandro
- Año de publicación
- 2005
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let B be a von Neumann algebra and X a C* Hilbert B-module. If p ∈ B is a projection, denote by S_p(X) ={x ∈ X(x,x) =p}, the p-sphere of X. For φ a state of B with support p ∈ B and x ∈ S_p(X), consider the state φ_x of L_B(X) given by φ_x(t)=φ((x,t(x))). In this paper we study certain sets associated to these states, and examine their topologic properties. As an application of these techniques, we prove that the space of states of the hyperfinite II_1 factor R_0, with support equivalent to a given projection p ∈ R_0, regarded with the norm topology (of the conjugate space of R_0), has trivial homotopy groups of all orders.
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina - Materia
-
STATE SPACE
C*-MODULE - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
.jpg)
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/106949
Ver los metadatos del registro completo
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States with equivalent supportsAndruchow, EstebanVarela, AlejandroSTATE SPACEC*-MODULEhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let B be a von Neumann algebra and X a C* Hilbert B-module. If p ∈ B is a projection, denote by S_p(X) ={x ∈ X(x,x) =p}, the p-sphere of X. For φ a state of B with support p ∈ B and x ∈ S_p(X), consider the state φ_x of L_B(X) given by φ_x(t)=φ((x,t(x))). In this paper we study certain sets associated to these states, and examine their topologic properties. As an application of these techniques, we prove that the space of states of the hyperfinite II_1 factor R_0, with support equivalent to a given projection p ∈ R_0, regarded with the norm topology (of the conjugate space of R_0), has trivial homotopy groups of all orders.Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaTheta Foundation2005-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/106949Andruchow, Esteban; Varela, Alejandro; States with equivalent supports; Theta Foundation; Journal Of Operator Theory; 53; 1; 12-2005; 35-480379-4024CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.theta.ro/jot/archive/2005-053-001/2005-053-001-002.htmlinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:52:44Zoai:ri.conicet.gov.ar:11336/106949instacron: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:34982025-10-22 11:52:44.656CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
States with equivalent supports |
| title |
States with equivalent supports |
| spellingShingle |
States with equivalent supports Andruchow, Esteban STATE SPACE C*-MODULE |
| title_short |
States with equivalent supports |
| title_full |
States with equivalent supports |
| title_fullStr |
States with equivalent supports |
| title_full_unstemmed |
States with equivalent supports |
| title_sort |
States with equivalent supports |
| dc.creator.none.fl_str_mv |
Andruchow, Esteban Varela, Alejandro |
| author |
Andruchow, Esteban |
| author_facet |
Andruchow, Esteban Varela, Alejandro |
| author_role |
author |
| author2 |
Varela, Alejandro |
| author2_role |
author |
| dc.subject.none.fl_str_mv |
STATE SPACE C*-MODULE |
| topic |
STATE SPACE C*-MODULE |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
Let B be a von Neumann algebra and X a C* Hilbert B-module. If p ∈ B is a projection, denote by S_p(X) ={x ∈ X(x,x) =p}, the p-sphere of X. For φ a state of B with support p ∈ B and x ∈ S_p(X), consider the state φ_x of L_B(X) given by φ_x(t)=φ((x,t(x))). In this paper we study certain sets associated to these states, and examine their topologic properties. As an application of these techniques, we prove that the space of states of the hyperfinite II_1 factor R_0, with support equivalent to a given projection p ∈ R_0, regarded with the norm topology (of the conjugate space of R_0), has trivial homotopy groups of all orders. Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina Fil: Varela, Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina |
| description |
Let B be a von Neumann algebra and X a C* Hilbert B-module. If p ∈ B is a projection, denote by S_p(X) ={x ∈ X(x,x) =p}, the p-sphere of X. For φ a state of B with support p ∈ B and x ∈ S_p(X), consider the state φ_x of L_B(X) given by φ_x(t)=φ((x,t(x))). In this paper we study certain sets associated to these states, and examine their topologic properties. As an application of these techniques, we prove that the space of states of the hyperfinite II_1 factor R_0, with support equivalent to a given projection p ∈ R_0, regarded with the norm topology (of the conjugate space of R_0), has trivial homotopy groups of all orders. |
| publishDate |
2005 |
| dc.date.none.fl_str_mv |
2005-12 |
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info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion http://purl.org/coar/resource_type/c_6501 info:ar-repo/semantics/articulo |
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article |
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publishedVersion |
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http://hdl.handle.net/11336/106949 Andruchow, Esteban; Varela, Alejandro; States with equivalent supports; Theta Foundation; Journal Of Operator Theory; 53; 1; 12-2005; 35-48 0379-4024 CONICET Digital CONICET |
| url |
http://hdl.handle.net/11336/106949 |
| identifier_str_mv |
Andruchow, Esteban; Varela, Alejandro; States with equivalent supports; Theta Foundation; Journal Of Operator Theory; 53; 1; 12-2005; 35-48 0379-4024 CONICET Digital CONICET |
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eng |
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eng |
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info:eu-repo/semantics/altIdentifier/url/https://www.theta.ro/jot/archive/2005-053-001/2005-053-001-002.html |
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info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ |
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openAccess |
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Theta Foundation |
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Theta Foundation |
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