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Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces

Azagra Rueda, Daniel and Fry, Robb and Montesinos Matilla, Luis Alejandro (2004) Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces. Proceedings of the American Mathematical Society, 133 (3). pp. 727-734. ISSN 1088-6826

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Abstract

We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have C-p-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y boolean AND U --> R and every epsilon > 0, there exists a C-p-smooth Lipschitz function F : X --> R such that |F(y)- f( y)| less than or equal to epsilon for every y is an element of Y boolean AND U.


Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:13962
Deposited On:25 Nov 2011 12:26
Last Modified:06 Feb 2014 09:56

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