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Título:
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Characterization of a Banach-Finsler manifold in terms of the algebras of smooth functions
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Autores:
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Jaramillo Aguado, Jesús Ángel ;
Jiménez Sevilla, María del Mar ;
Sánchez González, L.
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Tipo de documento:
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texto impreso
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Editorial:
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American Mathematical Society, 2014-03
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Dimensiones:
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application/pdf
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Nota general:
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info:eu-repo/semantics/openAccess
info:eu-repo/semantics/embargoedAccess
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Idiomas:
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Palabras clave:
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Estado = Publicado
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Materia = Ciencias: Matemáticas: Análisis matemático
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Tipo = Artículo
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Resumen:
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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).
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En línea:
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https://eprints.ucm.es/id/eprint/24700/1/JimenezSevilla200libre.pdf
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