This is an announcement for the paper "Corrigendum to Approximation by C^{p}-smooth, Lipschitz functions on Banach spaces" [J. Math. Anal. Appl., 315 (2006), 599-605]" by R. Fry.

Abstract: In this erratum, we recover the results from an earlier paper of the author's which contained a gap. Specifically, we prove that if X is a Banach space with an unconditional basis and admits a C^{p}-smooth, Lipschitz bump function, and Y is a convex subset of X, then any uniformly continuous function f: Y->R can be uniformly approximated by Lipschitz, C^{p}-smooth functions K:X->R. Also, if Z is any Banach space and f:X->Z is L-Lipschitz, then the approximates K:X->Z can be chosen CL-Lipschitz and C^{p}-smooth, for some constant C depending only on X.

Archive classification: math.FA

Mathematics Subject Classification: 46B20

Citation: Journal of Mathematical Analysis and Applications, Volume 348,

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/0810.3881

or

http://arXiv.org/abs/0810.3881

or by email in unzipped form by transmitting an empty message with subject line

uget 0810.3881

or in gzipped form by using subject line

get 0810.3881

to: math@arXiv.org.