Some properties of the injective tensor product of \(L^{p}\)[0,1] and a Banach space.
Let \(X\) be a Banach space. The method of [\textit{Q. Bu, J. Diestel}, Quaest. Math. 24, 519--533 (2001; Zbl 1038.46061)], [\textit{Q. Bu}, Quaest. Math. 25, 209--227 (2002; Zbl 1038.46060)], and [\textit{Q. Bu, P.-N. Dowling}, Quaest. Math. 25, 303--310 (2002; Zbl 1038.46062)] is developed further to prove that the injective tensor product \(L_p(0,1)\check\otimes X, 1<p<\infty\), has the Radon--Nikodým property, the analytic Radon--Nikodým property, the near Radon--Nikodým property, does not contain a copy of \(c_0\), or is weakly sequentially complete if and only if \(X\) has the same property and each bounded linear operator from \(L_q(0,1)\) to \(X\) is compact, where \(1/p+1/q=1\).
scientific article; zbMATH DE number 2005486
scientific article