Stability of Banach Space Properties In The Projective Tensor Product

Abstract

Let X be a real or complex Banach space and 1 < p < ∞. We show that L ^p [0, 1] ⊗ X has a property (P) whenever X has property (P), provided that (P) has certain characteristics. Examples of property (P) are the Radon-Nikodym property, the analytic Radon-Nikodym property, the near Radon-Nikodym property, the complete continuity property, the analytic complete continuity property, and the property of not containing a copy of c ₀.