Smooth norms and approximation in Banach spaces of the type C(K)
Functional Analysis
2007-05-23 v1
Abstract
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).
Keywords
Cite
@article{arxiv.math/0610421,
title = {Smooth norms and approximation in Banach spaces of the type C(K)},
author = {Petr Hajek and Richard Haydon},
journal= {arXiv preprint arXiv:math/0610421},
year = {2007}
}