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 The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.FA/0610421 or http://arXiv.org/abs/math.FA/0610421 or by email in unzipped form by transmitting an empty message with subject line uget 0610421 or in gzipped form by using subject line get 0610421 to: math@arXiv.org.