Approximation by Cp-smooth, Lipschitz functions on Banach spaces ✩

If X is a Banach space with an unconditional basis and admits a Cp-smooth, Lipschitz bump function, and Y is a subset of X, then any uniformly continuous function on Y can be uniformly approximated by functions which are Cp-smooth and Lipschitz on X.  2005 Elsevier Inc. All rights reserved