Approximation of Lipschitz functions by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces

Details Approximation of Lipschitz functions by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces Approximation of Lipschitz functions by Lipschitz, C^{p} smooth functions on weakly compactly generated Banach spaces

2009-07-01

arxiv.org/abs/0907.0241v4

Mathematics

Functional Analysis

Added comments, a few corrections. 16 pages

Scientific paper

This note corrects a gap and improves results in an earlier paper by the first named author. 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. Moreover, 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.

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