Perturbed smooth Lipschitz extensions of uniformly continuous functions on Banach spaces
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- by Daniel Azagra, Robb Fry and Alejandro Montesinos PDF
- Proc. Amer. Math. Soc. 133 (2005), 727-734 Request permission
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 $f:Y\cap U\to \mathbb {R}$ and every $\varepsilon >0$, there exists a $C^p$-smooth Lipschitz function $F:X\to \mathbb {R}$ such that $|F(y)-f(y)|\leq \varepsilon$ for every $y\in Y\cap U$.References
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Additional Information
- Daniel Azagra
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
- Email: daniel_azagra@mat.ucm.es
- Robb Fry
- Affiliation: Department of Mathematics and Computer Science, St. Francis Xavier University, P.O. Box 5000, Antigonish, Nova Scotia, Canada B2G 2W5
- Email: rfry@stfx.ca
- Alejandro Montesinos
- Affiliation: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense, 28040 Madrid, Spain
- Email: a_montesinos@mat.ucm.es
- Received by editor(s): January 26, 2003
- Published electronically: October 21, 2004
- Communicated by: Jonathan M. Borwein
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 727-734
- MSC (2000): Primary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-04-07715-9
- MathSciNet review: 2113921