This is an announcement for the paper "Smooth norms and approximation in Banach spaces of the type C(K)" by Petr Hajek and Richard Haydon.

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^m (except at 0).

Archive classification: Functional Analysis

Mathematics Subject Classification: 46B03; 46B26

The source file(s), SmoothNormsAndApprox.tex: 25237 bytes, is(are) stored in gzipped form as 0610421.gz with size 9kb. The corresponding postcript file has gzipped size 46kb.

Submitted from: richard.haydon@bnc.ox.ac.uk

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