Geometry of the projective unitary group of a C*-algebra

Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.

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Autor principal: Andruchow, Esteban
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: Unión Matemática Argentina 2024
Materias:
C*-Algebra
Projective unitaries
Acceso en línea:http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1810
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Repositorio Institucional Digital de Acceso Abierto (UNGS) de Universidad Nacional de General Sarmiento
id I71-R177-UNGS-1810
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spelling I71-R177-UNGS-18102024-12-23T13:21:48Z Geometry of the projective unitary group of a C*-algebra Andruchow, Esteban C*-Algebra Projective unitaries 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 C*-algebra with a faithful state ?. It is proved thatthe projective unitary group P UA of A,P UA = UA/T.1,(UA denotes the unitary group of A) is a C?-submanifold of the Banach spaceBs(A) of bounded operators acting in A, which are symmetric for the ?-innerproduct, and are usually called symmetrizable linear operators in A.A quotient Finsler metric is introduced in P UA, following the theory ofhomogeneous spaces of the unitary group of a C*-algebra. Curves of minimallength with any given initial conditions are exhibited. Also it is proved that ifA is a von Neumann algebra (or more generally, an algebra where the unitarygroup is exponential) two elements in P UA can be joined by a minimal curve.In the case when A is a von Neumann algebra with a finite trace, theseminimality results hold for the quotient of the metric induced by the p-normof the trace (p ? 2), which metrizes the strong operator topology of P UA. 2024-12-23T13:21:48Z 2024-12-23T13:21:48Z 2017 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. (2017). Geometry of the projective unitary group of a C*-algebra. Revista de la Unión Matemática Argentina, 58(2), 319-329. 0041-6932 http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1810 eng info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf Unión Matemática Argentina Revista de la Unión Matemática Argentina. Jun. 2017; 58(2): 319-329 https://inmabb.criba.edu.ar/revuma/revuma.php?p=toc/vol58
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 C*-Algebra
Projective unitaries
spellingShingle C*-Algebra
Projective unitaries
Andruchow, Esteban
Geometry of the projective unitary group of a C*-algebra
topic_facet C*-Algebra
Projective unitaries
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 Geometry of the projective unitary group of a C*-algebra
title_short Geometry of the projective unitary group of a C*-algebra
title_full Geometry of the projective unitary group of a C*-algebra
title_fullStr Geometry of the projective unitary group of a C*-algebra
title_full_unstemmed Geometry of the projective unitary group of a C*-algebra
title_sort geometry of the projective unitary group of a c*-algebra
publisher Unión Matemática Argentina
publishDate 2024
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1810
work_keys_str_mv AT andruchowesteban geometryoftheprojectiveunitarygroupofacalgebra
_version_ 1824528660650000384

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