Observations About the Projective Tensor Product of Banach Spaces, Iii – L^P [0, 1] ⊗ X, 1 < P < ∞

Abstract

Let X be a complex Banach space and 1 < p < ∞. Then the projective tensor product L ^p [0, 1]⊗ X has the analytic Radon-Nikodym property (respectively, the near Radon-Nikodym property) if and only if X does. Also, L ^p[0, 1]⊗ X does not contain a copy of c ₀ if and only if X does not contain a copy of c ₀.