The Poincaré half-space of a C∗-algebra
- Autores
- Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro
- Año de publicación
- 2019
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- Let A be a unital C*-algebra. Given a faithful representation A⊂B(L) in a Hilbert space L, the set G^+⊂A of positive invertible elements can be thought of as the set of inner products in L, related to A, which are equivalent to the original inner product. The set G^+ has a rich geometry, it is a homogeneous space of the invertible group G of A, with an invariant Finsler metric. In the present paper we study the tangent bundle TG^+ of G^+, as a homogenous Finsler space of a natural group of invertible matrices in M_2(A), identifying TG^+ with the it Poincaré half-space H of A. H={H ∈ A : Im(h)≥ 0,Im(h) invertible}. We show that H≃TG^+ has properties similar to those of a space of non-positive constant curvature.
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. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simon Bolivar.; Venezuela - Materia
-
POSITIVE INVERTIBLE OPERATOR
INNER PRODUCT - 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:11336/108159
Ver los metadatos del registro completo
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The Poincaré half-space of a C∗-algebraAndruchow, EstebanCorach, GustavoRecht, LázaroPOSITIVE INVERTIBLE OPERATORINNER PRODUCThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Let A be a unital C*-algebra. Given a faithful representation A⊂B(L) in a Hilbert space L, the set G^+⊂A of positive invertible elements can be thought of as the set of inner products in L, related to A, which are equivalent to the original inner product. The set G^+ has a rich geometry, it is a homogeneous space of the invertible group G of A, with an invariant Finsler metric. In the present paper we study the tangent bundle TG^+ of G^+, as a homogenous Finsler space of a natural group of invertible matrices in M_2(A), identifying TG^+ with the it Poincaré half-space H of A. H={H ∈ A : Im(h)≥ 0,Im(h) invertible}. We show that H≃TG^+ has properties similar to those of a space of non-positive constant curvature.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. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simon Bolivar.; VenezuelaUniversidad Autónoma de Madrid2019-08info: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/11336/108159Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; The Poincaré half-space of a C∗-algebra; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 35; 7; 8-2019; 2187-22190213-2230CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.ems-ph.org/journals/show_abstract.php?issn=0213-2230&vol=35&iss=7&rank=13/rmi/1117info:eu-repo/semantics/altIdentifier/doi/10.4171/rmi/1117info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1711.08802info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-10T13:18:50Zoai:ri.conicet.gov.ar:11336/108159instacron: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:34982025-09-10 13:18:51.493CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse |
| dc.title.none.fl_str_mv |
The Poincaré half-space of a C∗-algebra |
| title |
The Poincaré half-space of a C∗-algebra |
| spellingShingle |
The Poincaré half-space of a C∗-algebra Andruchow, Esteban POSITIVE INVERTIBLE OPERATOR INNER PRODUCT |
| title_short |
The Poincaré half-space of a C∗-algebra |
| title_full |
The Poincaré half-space of a C∗-algebra |
| title_fullStr |
The Poincaré half-space of a C∗-algebra |
| title_full_unstemmed |
The Poincaré half-space of a C∗-algebra |
| title_sort |
The Poincaré half-space of a C∗-algebra |
| 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 |
POSITIVE INVERTIBLE OPERATOR INNER PRODUCT |
| topic |
POSITIVE INVERTIBLE OPERATOR INNER PRODUCT |
| 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 A be a unital C*-algebra. Given a faithful representation A⊂B(L) in a Hilbert space L, the set G^+⊂A of positive invertible elements can be thought of as the set of inner products in L, related to A, which are equivalent to the original inner product. The set G^+ has a rich geometry, it is a homogeneous space of the invertible group G of A, with an invariant Finsler metric. In the present paper we study the tangent bundle TG^+ of G^+, as a homogenous Finsler space of a natural group of invertible matrices in M_2(A), identifying TG^+ with the it Poincaré half-space H of A. H={H ∈ A : Im(h)≥ 0,Im(h) invertible}. We show that H≃TG^+ has properties similar to those of a space of non-positive constant curvature. 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. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina. Universidad Simon Bolivar.; Venezuela |
| description |
Let A be a unital C*-algebra. Given a faithful representation A⊂B(L) in a Hilbert space L, the set G^+⊂A of positive invertible elements can be thought of as the set of inner products in L, related to A, which are equivalent to the original inner product. The set G^+ has a rich geometry, it is a homogeneous space of the invertible group G of A, with an invariant Finsler metric. In the present paper we study the tangent bundle TG^+ of G^+, as a homogenous Finsler space of a natural group of invertible matrices in M_2(A), identifying TG^+ with the it Poincaré half-space H of A. H={H ∈ A : Im(h)≥ 0,Im(h) invertible}. We show that H≃TG^+ has properties similar to those of a space of non-positive constant curvature. |
| publishDate |
2019 |
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2019-08 |
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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/11336/108159 Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; The Poincaré half-space of a C∗-algebra; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 35; 7; 8-2019; 2187-2219 0213-2230 CONICET Digital CONICET |
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http://hdl.handle.net/11336/108159 |
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Andruchow, Esteban; Corach, Gustavo; Recht, Lázaro; The Poincaré half-space of a C∗-algebra; Universidad Autónoma de Madrid; Revista Matematica Iberoamericana; 35; 7; 8-2019; 2187-2219 0213-2230 CONICET Digital CONICET |
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eng |
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eng |
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