This is an announcement for the paper "Corrigendum to [Approximation by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces, J. Funct. Anal. 252 (2007), no. 1, 34--41.]" by R. Fry and L. Keener.
Abstract: This note is a corrigendum to an earlier paper by the first named author. The original proof contained a gap which is here corrected under the formally stronger hypothesis that X admit a C^{p} smooth norm rather than merely a Lipschitz, C^{p} smooth bump function. More precisely, it is shown that on weakly compactly generated Banach spaces X which admit a C^{p} smooth norm, one can uniformly approximate uniformly continuous functions f:X->R by Lipschitz, C^{p} smooth functions. Additionally it is shown in this note that there is a constant C>1 so that any L-Lipschitz function f:X->R can be uniformly approximated by CL-Lipschitz, C^{p} smooth functions. This provides a `Lipschitz version' of the classical approximation results of Godefroy, Troyanski, Whitfield and Zizler.
Archive classification: math.FA
Mathematics Subject Classification: 46B20
The source file(s), LIPWCGJune3009.tex: 45249 bytes, is(are) stored in gzipped form as 0907.0241.gz with size 12kb. The corresponding postcript file has gzipped size 98kb.
Submitted from: rfry@tru.ca
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