Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4592151 | Journal of Functional Analysis | 2010 | 22 Pages |
Abstract
We prove, among other things, that a Lipschitz (or uniformly continuous) mapping f:X→Y can be approximated (even in a fine topology) by smooth Lipschitz (resp. uniformly continuous) mapping, if X is a separable Banach space admitting a smooth Lipschitz bump and either X or Y is a separable C(K) space (resp. super-reflexive space). Further, we show how smooth approximation of Lipschitz mappings is closely related to a smooth approximation of C1-smooth mappings together with their first derivatives. As a corollary we obtain new results on smooth approximation of C1-smooth mappings together with their first derivatives.
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