Some properties of the injective tensor product of L-P[0,1] and a Banach space

摘要

Let X be a (real or complex) Banach space and 1< p,p' < infinity such that 1/p + 1/p' = 1. Then L-p[0, 1]circle timesX, the injective tensor product of L-p[0, 1] and X, has the Radon-Nikodym property (resp. the analytic Radon-Nikodym property, the near Radon-Nikodym property, contains no copy of c(0), is weakly sequentially complete) if and only if X has the same property and each continuous linear operator from L-p' [0, 1] to X is compact. (C) 2003 Elsevier Inc. All rights reserved. [References: 23]