Original Articles

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

Published in: Quaestiones Mathematicae
Volume 25, issue 2, 2002 , pages: 209–227
DOI: 10.2989/16073600209486010
Author(s): Qingying Bu

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.

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