The Poincaré half-space of a C*-algebra
- Autores
- Andruchow, Esteban
- 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.
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 homogeneous Finsler space of a natural group of invertible matrices in M2(A), identifying TG+ with the 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. - Fuente
- Revista Matemática Iberoamericana 2019; 35(7): 2187–2219
https://ems.press/journals/rmi/issues/652 - Materia
-
Positive invertible operator
Inner product - Nivel de accesibilidad
- acceso restringido
- 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/1805
Ver los metadatos del registro completo
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The Poincaré half-space of a C*-algebraAndruchow, EstebanPositive invertible operatorInner productFil: 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.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 homogeneous Finsler space of a natural group of invertible matrices in M2(A), identifying TG+ with the 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.Universidad Autónoma de Madrid2024-12-23T13:21:47Z2024-12-23T13:21:47Z2019info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfAndruchow, E., Corach, G. y Recht, L. (2019). The Poincaré half-space of a C*-algebra. Revista Matemática Iberoamericana; 35(7), 2187–2219.0213-2230http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1805Revista Matemática Iberoamericana 2019; 35(7): 2187–2219https://ems.press/journals/rmi/issues/652reponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoeng10.4171/RMI/1117info:eu-repo/semantics/restrictedAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2025-10-16T15:29:12Zoai:repositorio.ungs.edu.ar:UNGS/1805instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2025-10-16 15:29:13.247Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse |
| 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 |
| author |
Andruchow, Esteban |
| author_facet |
Andruchow, Esteban |
| author_role |
author |
| dc.subject.none.fl_str_mv |
Positive invertible operator Inner product |
| topic |
Positive invertible operator Inner product |
| 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. 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 homogeneous Finsler space of a natural group of invertible matrices in M2(A), identifying TG+ with the 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. |
| 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). The Poincaré half-space of a C*-algebra. Revista Matemática Iberoamericana; 35(7), 2187–2219. 0213-2230 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1805 |
| identifier_str_mv |
Andruchow, E., Corach, G. y Recht, L. (2019). The Poincaré half-space of a C*-algebra. Revista Matemática Iberoamericana; 35(7), 2187–2219. 0213-2230 |
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http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1805 |
| dc.language.none.fl_str_mv |
eng |
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eng |
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10.4171/RMI/1117 |
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info:eu-repo/semantics/restrictedAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ |
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restrictedAccess |
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https://creativecommons.org/licenses/by-nc-nd/4.0/ |
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application/pdf |
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Universidad Autónoma de Madrid |
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Universidad Autónoma de Madrid |
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Revista Matemática Iberoamericana 2019; 35(7): 2187–2219 https://ems.press/journals/rmi/issues/652 reponame:Repositorio Institucional UNGS instname:Universidad Nacional de General Sarmiento |
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Repositorio Institucional UNGS - Universidad Nacional de General Sarmiento |
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ubyd@campus.ungs.edu.ar |
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