Locally uniformly convex norms in Banach spaces and their duals
Functional Analysis
2007-05-23 v2 General Topology
Abstract
It is shown that a Banach space with locally uniformly convex dual 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.
Keywords
Cite
@article{arxiv.math/0610420,
title = {Locally uniformly convex norms in Banach spaces and their duals},
author = {Richard Haydon},
journal= {arXiv preprint arXiv:math/0610420},
year = {2007}
}
Comments
The abstract has now been corrected