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.

The abstract has now been corrected

References in corpus (1)

• Smooth norms and approximation in Banach spaces of the type C(K)