Metrics in the sphere of a Hilbert C*-module
- Autores
- Andruchow, Esteban; Varela, Alejandro
- Año de publicación
- 2007
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Given a unital C∗-algebra A and a right C∗-module X over A, we consider the problem of finding short smooth curves in the sphere SX = {x ∈ X :( x, x) = 1}. Curves in SX are measured considering the Finsler metric which consists of the norm of X at each tangent space of SX, The initial x0 ∈ Sx and any tangent vector υ at x0, there exists a curve γ(t)=e^tZ(x0), Z ∈ LA(X), Z*=-Z and ∥Z∥ ≤ π, such that γ(0)=υ, which is minimizing along its path for t ∈ [0,1]. the existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the boundary value problem given x0, x1 ∈ SX , find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us denote by ƒ0 the selfadjoint projection I − x0 ⊗ x0, if the algebra ƒ0LA(X)ƒ0 is finite dimensional, then there exists a curve γ, which is minimizing along its path.
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: 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
-
C*MODULES
SPHERES
GEODESICS - 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:11336/101032
Ver los metadatos del registro completo
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Metrics in the sphere of a Hilbert C*-moduleAndruchow, EstebanVarela, AlejandroC*MODULESSPHERESGEODESICShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Given a unital C∗-algebra A and a right C∗-module X over A, we consider the problem of finding short smooth curves in the sphere SX = {x ∈ X :( x, x) = 1}. Curves in SX are measured considering the Finsler metric which consists of the norm of X at each tangent space of SX, The initial x0 ∈ Sx and any tangent vector υ at x0, there exists a curve γ(t)=e^tZ(x0), Z ∈ LA(X), Z*=-Z and ∥Z∥ ≤ π, such that γ(0)=υ, which is minimizing along its path for t ∈ [0,1]. the existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the boundary value problem given x0, x1 ∈ SX , find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us denote by ƒ0 the selfadjoint projection I − x0 ⊗ x0, if the algebra ƒ0LA(X)ƒ0 is finite dimensional, then there exists a curve γ, which is minimizing along its path.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: 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; ArgentinaVersita2007-12info: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/11336/101032Andruchow, Esteban; Varela, Alejandro; Metrics in the sphere of a Hilbert C*-module; Versita; Central European Journal of Mathematics - (Online); 5; 4; 12-2007; 639-6531895-10741644-3616CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.2478/s11533-007-0025-1info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/journal/11533/5/4info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:04:38Zoai:ri.conicet.gov.ar:11336/101032instacron: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 10:04:38.825CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
Metrics in the sphere of a Hilbert C*-module |
| title |
Metrics in the sphere of a Hilbert C*-module |
| spellingShingle |
Metrics in the sphere of a Hilbert C*-module Andruchow, Esteban C*MODULES SPHERES GEODESICS |
| title_short |
Metrics in the sphere of a Hilbert C*-module |
| title_full |
Metrics in the sphere of a Hilbert C*-module |
| title_fullStr |
Metrics in the sphere of a Hilbert C*-module |
| title_full_unstemmed |
Metrics in the sphere of a Hilbert C*-module |
| title_sort |
Metrics in the sphere of a Hilbert C*-module |
| 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 |
C*MODULES SPHERES GEODESICS |
| topic |
C*MODULES SPHERES GEODESICS |
| purl_subject.fl_str_mv |
https://purl.org/becyt/ford/1.1 https://purl.org/becyt/ford/1 |
| dc.description.none.fl_txt_mv |
Given a unital C∗-algebra A and a right C∗-module X over A, we consider the problem of finding short smooth curves in the sphere SX = {x ∈ X :( x, x) = 1}. Curves in SX are measured considering the Finsler metric which consists of the norm of X at each tangent space of SX, The initial x0 ∈ Sx and any tangent vector υ at x0, there exists a curve γ(t)=e^tZ(x0), Z ∈ LA(X), Z*=-Z and ∥Z∥ ≤ π, such that γ(0)=υ, which is minimizing along its path for t ∈ [0,1]. the existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the boundary value problem given x0, x1 ∈ SX , find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us denote by ƒ0 the selfadjoint projection I − x0 ⊗ x0, if the algebra ƒ0LA(X)ƒ0 is finite dimensional, then there exists a curve γ, which is minimizing along its path. 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: 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 |
Given a unital C∗-algebra A and a right C∗-module X over A, we consider the problem of finding short smooth curves in the sphere SX = {x ∈ X :( x, x) = 1}. Curves in SX are measured considering the Finsler metric which consists of the norm of X at each tangent space of SX, The initial x0 ∈ Sx and any tangent vector υ at x0, there exists a curve γ(t)=e^tZ(x0), Z ∈ LA(X), Z*=-Z and ∥Z∥ ≤ π, such that γ(0)=υ, which is minimizing along its path for t ∈ [0,1]. the existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the boundary value problem given x0, x1 ∈ SX , find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us denote by ƒ0 the selfadjoint projection I − x0 ⊗ x0, if the algebra ƒ0LA(X)ƒ0 is finite dimensional, then there exists a curve γ, which is minimizing along its path. |
| publishDate |
2007 |
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2007-12 |
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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/11336/101032 Andruchow, Esteban; Varela, Alejandro; Metrics in the sphere of a Hilbert C*-module; Versita; Central European Journal of Mathematics - (Online); 5; 4; 12-2007; 639-653 1895-1074 1644-3616 CONICET Digital CONICET |
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http://hdl.handle.net/11336/101032 |
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Andruchow, Esteban; Varela, Alejandro; Metrics in the sphere of a Hilbert C*-module; Versita; Central European Journal of Mathematics - (Online); 5; 4; 12-2007; 639-653 1895-1074 1644-3616 CONICET Digital CONICET |
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eng |
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eng |
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