Observations About the Projective Tensor Product of Banach Spaces, Iii – LP [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.