## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# Perturbed Smooth Lipschitz Extensions of Uniformly Continuous Functions on Banach Spaces

Daniel Azagra, Robb Fry and Alejandro Montesinos
Proceedings of the American Mathematical Society
Vol. 133, No. 3 (Mar., 2005), pp. 727-734
Stable URL: http://www.jstor.org/stable/4097746
Page Count: 8
Preview not available

## 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 $f : Y \cap U \rightarrow \mathbb{R}$ and every $\varepsilon > 0$, there exists a $C^{p}-smooth$ Lipschitz function $F : X \rightarrow \mathbb{R}$ such that $\left \vert F(y) - f(y)\right \vert \leq \varepsilon$ for every $y \in Y \cap U$.

• 727
• 728
• 729
• 730
• 731
• 732
• 733
• 734