This is an announcement for the paper "Locally uniformly convex norms in Banach spaces and their duals" by Richard Haydon.

Abstract: It is shown that a Banach space with locally uniformly convex norm admits an equivalent norm which is itself locally uniformly convex. It follows that on any such space all continuous real-valued functions may be uniformly approximated by C^1 functions.

Archive classification: Functional Analysis; General Topology

Mathematics Subject Classification: 46B20

The source file(s), LURnormsAndDuals.tex: 50635 bytes, is(are) stored in gzipped form as 0610420.gz with size 15kb. The corresponding postcript file has gzipped size 65kb.

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/0610420

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http://arXiv.org/abs/math.FA/0610420

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uget 0610420

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