Smooth approximations |
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Authors: | Petr Há jek |
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Affiliation: | a Mathematical Institute, Czech Academy of Science, ?itná 25, 115 67 Praha 1, Czech Republic b Department of Mathematical Analysis, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic |
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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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Keywords: | Smoothness Approximation Lipschitz |
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