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Lipschitz-type functions on metric spaces

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Garrido, M. Isabel y Jaramillo Aguado, Jesús Ángel (2008) Lipschitz-type functions on metric spaces. Journal of Mathematical Analysis and Applications, 340 (1). pp. 282-290. ISSN 0022-247X

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URL Oficial: http://www.sciencedirect.com/science/article/pii/S0022247X0701044X


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Resumen

In order to find metric spaces X for which the algebra Lip*(X) of bounded Lipschitz functions on X determines the Lipschitz structure of X, we introduce the class of small-determined spaces. We show that this class includes precompact and quasi-convex metric spaces. We obtain several metric characterizations of this property, as well as some other characterizations given in terms of the uniform approximation and the extension of uniformly continuous functions. In particular we show that X is small-determined if and only if every uniformly continuous real function on X can be uniformly approximated by Lipschitz functions.


Tipo de documento:Artículo
Palabras clave:Banach-Stone theorem; Lipschitz functions; small-determined metric space; uniform approximation
Materias:Ciencias > Matemáticas > Análisis funcional y teoría de operadores
Código ID:16329
Depositado:12 Sep 2012 11:06
Última Modificación:27 May 2016 14:15

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