Uniform Convexity of Köthe-Bochner function spaces

Abstract

Of concern are the Köthe-Bochner function spaces E(X) where X is a real Banach space. Thus, of concern is the uniform convexity on the Köthe-Bochner function space E(X). We show that E(X) is uniformly convex if and only if both spaces E and X are uniformly convex. It is the uniform convexity that is the focal point