منابع مشابه
Smooth Approximations
We prove that a Lipschitz (or uniformly continuous) mapping f : X → Y can be approximated 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 C(K) space (resp. super-reflexive space). As a corollary we obtain also smooth approximation of C1-smooth mappings together with their first derivatives.
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Let X be a WCG Banach space admitting a Ck-Fréchet smooth norm. Then X admits an equivalent norm which is simultaneously C1-Fréchet smooth, LUR, and a uniform limit of Ck-Fréchet smooth norms. If X = C([0, α]), where α is an ordinal, then the same conclusion holds true with k =∞.
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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2010
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2010.04.020