Larotonda spaces : homogeneous spaces and conditional expectations

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

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Detalles Bibliográficos
Autores principales: Andruchow, Esteban, Recht, Lázaro
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: World Scientific 2024
Materias:
Finsler Metric
Geodesic
Homogeneous Space
Unitary Group of A C-Algebra
Acceso en línea:http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1813
Aporte de:
Repositorio Institucional Digital de Acceso Abierto (UNGS) de Universidad Nacional de General Sarmiento
id I71-R177-UNGS-1813
record_format dspace
spelling I71-R177-UNGS-18132024-12-23T14:21:51Z Larotonda spaces : homogeneous spaces and conditional expectations Andruchow, Esteban Recht, Lázaro Finsler Metric Geodesic Homogeneous Space Unitary Group of A C-Algebra 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. Fil: Recht, Lázaro. Universidad de los Andes, Bogotá. Departamento de Matemáticas; Colombia. Fil: Recht, Lázaro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. We define a Larotonda space as a quotient space $P=U_A /U_B$ of the unitary groups of C*-algebras $1\in B\subset A$ with a faithful unital conditional expectation $$ \Phi:A\to B. $$ In particular, $B$ is complemented in $A$, a fact which implies that $P$ has $C^\infty$ differentiable structure, with the topology induced by the norm of $A$. The conditional expectation also allows one to define a reductive structure (in particular, a linear connection) and a $U_A$-invariant Finsler metric in $P$. given a point $\rho\in P$ and a tangent vector $X\in(T P)_\rho$, we consider the problem of wether the geodesic $\delta$ of the linear connection satisfying these inital data is (locally) minimal for the metric. We find a sufficient condition. Several examples are given, of locally minimal geodesics. 2024-12-23T14:17:58Z 2024-12-23T14:17:58Z 2016 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion Andruchow, E. y Recht, L. (2016). Larotonda spaces: homogeneous spaces and conditional expectations. International Journal Of Mathematics, 27(2), 1-17. 0129-167X http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1813 eng https://doi.org/10.1142/S0129167X16500026 info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf World Scientific Journal Of Mathematics. Feb. 2016; 27(2): 1-17 https://www.worldscientific.com/toc/ijm/27/02
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 Finsler Metric
Geodesic
Homogeneous Space
Unitary Group of A C-Algebra
spellingShingle Finsler Metric
Geodesic
Homogeneous Space
Unitary Group of A C-Algebra
Andruchow, Esteban
Recht, Lázaro
Larotonda spaces : homogeneous spaces and conditional expectations
topic_facet Finsler Metric
Geodesic
Homogeneous Space
Unitary Group of A C-Algebra
description Fil: Andruchow, Esteban. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
format Artículo
Artículo
publishedVersion
author Andruchow, Esteban
Recht, Lázaro
author_facet Andruchow, Esteban
Recht, Lázaro
author_sort Andruchow, Esteban
title Larotonda spaces : homogeneous spaces and conditional expectations
title_short Larotonda spaces : homogeneous spaces and conditional expectations
title_full Larotonda spaces : homogeneous spaces and conditional expectations
title_fullStr Larotonda spaces : homogeneous spaces and conditional expectations
title_full_unstemmed Larotonda spaces : homogeneous spaces and conditional expectations
title_sort larotonda spaces : homogeneous spaces and conditional expectations
publisher World Scientific
publishDate 2024
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1813
work_keys_str_mv AT andruchowesteban larotondaspaceshomogeneousspacesandconditionalexpectations
AT rechtlazaro larotondaspaceshomogeneousspacesandconditionalexpectations
_version_ 1824528698574897152

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