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
Repositorio Institucional UNGS
Institución
Universidad Nacional de General Sarmiento
OAI Identificador
oai:repositorio.ungs.edu.ar:UNGS/1805
Acceder
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oai_identifier_str oai:repositorio.ungs.edu.ar:UNGS/1805
network_acronym_str RIUNGS
repository_id_str
network_name_str Repositorio Institucional UNGS
spelling 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/4.0/2025-11-06T10:40:22Zoai: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:2025-11-06 10:40:22.792Repositorio 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
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1805
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.4171/RMI/1117
dc.rights.none.fl_str_mv info:eu-repo/semantics/restrictedAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv restrictedAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad Autónoma de Madrid
publisher.none.fl_str_mv Universidad Autónoma de Madrid
dc.source.none.fl_str_mv 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
reponame_str Repositorio Institucional UNGS
collection Repositorio Institucional UNGS
instname_str Universidad Nacional de General Sarmiento
repository.name.fl_str_mv Repositorio Institucional UNGS - Universidad Nacional de General Sarmiento
repository.mail.fl_str_mv ubyd@campus.ungs.edu.ar
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score 12.576249

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