Banach Spaces with Complete Continuity Properties

Abstract

Let X be a Banach space, (Ω, Σ, λ) be a finite measure space and G be a compact metrizable group. We discuss the complete continuity properties related to subsets of the dual group G for Bochner spaces. It is shown that if Λ is a Riesz-subset of G then L ^p (λ, X), where 1 ≤ p < ∞, has the type II-Λ-CCP whenever X does.