Locally uniformly convex norms in Banach spaces and their duals
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.
Related Researches
Submitted on 12 Oct 2006 (v1), last revised 14 Oct 2006 (this version, v2)
Updated
arXiv.org
Original Source