Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions

In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C-k Finsler manifold M is determined by the normed algebra C-b(k)(M) of all real-valued, bounded and C-k smooth functions with bounded derivative defined on M. As a consequence, we obtain: (i) the Fins...

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Detalles Bibliográficos
Autores: Jaramillo Aguado, Jesús Ángel, Jiménez Sevilla, María Del Mar, Sánchez González, L.
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33475
Acceso en línea:https://hdl.handle.net/20.500.14352/33475
Access Level:acceso abierto
Palabra clave:517
Differentiable functions
Riemannian-manifolds
Lipschitz functions
approximation
isometries
spaces
Análisis matemático
1202 Análisis y Análisis Funcional
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oai_identifier_str oai:docta.ucm.es:20.500.14352/33475
network_acronym_str ES
network_name_str España
repository_id_str
spelling Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functionsJaramillo Aguado, Jesús ÁngelJiménez Sevilla, María Del MarSánchez González, L.517Differentiable functionsRiemannian-manifoldsLipschitz functionsapproximationisometriesspacesAnálisis matemático1202 Análisis y Análisis FuncionalIn this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C-k Finsler manifold M is determined by the normed algebra C-b(k)(M) of all real-valued, bounded and C-k smooth functions with bounded derivative defined on M. As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete C-k Finsler manifold M is determined by the algebra C-b(k)(M); (ii) the weak Finsler structure of a separable and complete C-k Finsler manifold M modeled on a Banach space with a Lipschitz and C-k smooth bump function is determined by the algebra C-b(k)(M); (iii) the weak Finsler structure of a C-1 uniformly bumpable and complete C-1 Finsler manifold M modeled on a Weakly Compactly Generated (WCG) Banach space is determined by the algebra C-b(1)(M); and (iv) the isometric structure of a WCG Banach space X with a C-1 smooth bump function is determined by the algebra C-b(1)(X).American Mathematical SocietyUniversidad Complutense de Madrid20142014-03-0120142014-03-01journal articlehttp://purl.org/coar/resource_type/c_6501info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://hdl.handle.net/20.500.14352/33475reponame:Docta Complutenseinstname:Universidad Complutense de Madrid (UCM)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:docta.ucm.es:20.500.14352/334752026-06-02T12:44:21Z
dc.title.none.fl_str_mv Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
title Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
spellingShingle Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
Jaramillo Aguado, Jesús Ángel
517
Differentiable functions
Riemannian-manifolds
Lipschitz functions
approximation
isometries
spaces
Análisis matemático
1202 Análisis y Análisis Funcional
title_short Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
title_full Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
title_fullStr Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
title_full_unstemmed Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
title_sort Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
dc.creator.none.fl_str_mv Jaramillo Aguado, Jesús Ángel
Jiménez Sevilla, María Del Mar
Sánchez González, L.
author Jaramillo Aguado, Jesús Ángel
author_facet Jaramillo Aguado, Jesús Ángel
Jiménez Sevilla, María Del Mar
Sánchez González, L.
author_role author
author2 Jiménez Sevilla, María Del Mar
Sánchez González, L.
author2_role author
author
dc.contributor.none.fl_str_mv Universidad Complutense de Madrid
dc.subject.none.fl_str_mv 517
Differentiable functions
Riemannian-manifolds
Lipschitz functions
approximation
isometries
spaces
Análisis matemático
1202 Análisis y Análisis Funcional
topic 517
Differentiable functions
Riemannian-manifolds
Lipschitz functions
approximation
isometries
spaces
Análisis matemático
1202 Análisis y Análisis Funcional
description In this note we give sufficient conditions to ensure that the weak Finsler structure of a complete C-k Finsler manifold M is determined by the normed algebra C-b(k)(M) of all real-valued, bounded and C-k smooth functions with bounded derivative defined on M. As a consequence, we obtain: (i) the Finsler structure of a finite-dimensional and complete C-k Finsler manifold M is determined by the algebra C-b(k)(M); (ii) the weak Finsler structure of a separable and complete C-k Finsler manifold M modeled on a Banach space with a Lipschitz and C-k smooth bump function is determined by the algebra C-b(k)(M); (iii) the weak Finsler structure of a C-1 uniformly bumpable and complete C-1 Finsler manifold M modeled on a Weakly Compactly Generated (WCG) Banach space is determined by the algebra C-b(1)(M); and (iv) the isometric structure of a WCG Banach space X with a C-1 smooth bump function is determined by the algebra C-b(1)(X).
publishDate 2014
dc.date.none.fl_str_mv 2014
2014-03-01
2014
2014-03-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/20.500.14352/33475
url https://hdl.handle.net/20.500.14352/33475
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Mathematical Society
publisher.none.fl_str_mv American Mathematical Society
dc.source.none.fl_str_mv reponame:Docta Complutense
instname:Universidad Complutense de Madrid (UCM)
instname_str Universidad Complutense de Madrid (UCM)
reponame_str Docta Complutense
collection Docta Complutense
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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