[Banach] Abstract of a paper by Petr Hajek and Richard Haydon

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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