Observations About the Projective Tensor Product of Banach Spaces, II — L^p(0, 1) ⊗<i>X</i>, 1 &lt;<i>p</i>&lt; ∞

Abstract

In this paper, we first give a sequential representation of Lp (0, 1) ⊗ X, the projective tensor product of Lp (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.