Differentiation in Banach Spaces

Abstract

Publisher Summary This chapter provides an overview of differentiation in Banach spaces. A Banach space X has a boundedly complete basis (Xn) if each x ∊ X has the unique expansion. If X has a boundedly complete basis, then every Lipschitz is differentiable almost everywhere. Since Lipschitz functions have separable ranges, it is clear that a Banach space has Radon-Nikodym property (RNP) if and only if each of its separable subspaces has RNP. But each separable subspace of a reflexive space is a separable dual space and hence has the RNP.