The Poincaré half-space of a C*-algebra
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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Universidad Autónoma de Madrid
2024
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| Acceso en línea: | http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1805 |
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I71-R177-UNGS-18052024-12-23T13:21:47Z The Poincaré half-space of a C*-algebra Andruchow, Esteban Positive invertible operator Inner product 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. 2024-12-23T13:21:47Z 2024-12-23T13:21:47Z 2019 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion 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 eng 10.4171/RMI/1117 info:eu-repo/semantics/restrictedAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Universidad Autónoma de Madrid Revista Matemática Iberoamericana 2019; 35(7): 2187–2219 https://ems.press/journals/rmi/issues/652 |
| institution |
Universidad Nacional de General Sarmiento |
| institution_str |
I-71 |
| repository_str |
R-177 |
| collection |
Repositorio Institucional Digital de Acceso Abierto (UNGS) |
| language |
Inglés |
| orig_language_str_mv |
eng |
| topic |
Positive invertible operator Inner product |
| spellingShingle |
Positive invertible operator Inner product Andruchow, Esteban The Poincaré half-space of a C*-algebra |
| topic_facet |
Positive invertible operator Inner product |
| description |
Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. |
| format |
Artículo Artículo publishedVersion |
| author |
Andruchow, Esteban |
| author_facet |
Andruchow, Esteban |
| author_sort |
Andruchow, Esteban |
| title |
The Poincaré half-space of a C*-algebra |
| 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 |
poincaré half-space of a c*-algebra |
| publisher |
Universidad Autónoma de Madrid |
| publishDate |
2024 |
| url |
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1805 |
| work_keys_str_mv |
AT andruchowesteban thepoincarehalfspaceofacalgebra AT andruchowesteban poincarehalfspaceofacalgebra |
| _version_ |
1824528660119420928 |