Observations About the Projective Tensor Product of Banach Spaces, II — L^p(0, 1) ⊗X, 1 < p < ∞

Abstract

In this paper, we first give a sequential representation of L^p (0, 1) ⊗ X, the projective tensor product of L^p (0, 1) and a Banach space X. Then by this sequential representation, we show that L ^p (0, 1) ⊗ X, 1 < p < ∞, has the Radon-Nikodym property if X does. As a consequence, we also show that the injective tensor product L ^p (0, 1) ⊗ X, 1 < p < ∞, is an Asplund space if X is.