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arXiv:math/0610421 [math.FA]AbstractReferencesReviewsResources

Smooth norms and approximation in Banach spaces of the type C(K)

Petr Hajek, Richard Haydon

Published 2006-10-12Version 1

We prove two theorems about differentiable functions on the Banach space C(K), where K is compact. (i) If C(K) admits a non-trivial function of class C^m and of bounded support, then all continuous real-valued functions on C(K) may be uniformly approximated by functions of class C^m. (ii) If C(K) admits an equivalent norm with locally uniformly convex dual norm, then C(K) admits an equivalent norm which is of class C^infty (except at 0).

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