Some properties of the injective tensor product of \(L^{p}\)[0,1] and a Banach space.
type: Item
instance of: scholarly article
title: Some properties of the injective tensor product of \(L^{p}\)[0,1] and a Banach space.
zbMATH Open document ID: 1063.46060
DOI: 10.1016/S0022-1236(03)00098-3
author: Qingying Bu
published in: Journal of Functional Analysis
publication date: 2003-11-17T00:00:00Z
review text: 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 \(1/p+1/q=1\).
Mathematics Subject Classification ID: 46M05
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46B22
Mathematics Subject Classification ID: 46E40
zbMATH DE Number: 2005486
zbMATH Keywords: injective tensor product
zbMATH Keywords: Radon--Nikodým property
zbMATH Keywords: analytic Radon--Nikodým property
zbMATH Keywords: near Radon--Nikodým property
zbMATH Keywords: non-containment of \(c_0\)
reviewed by: Eve Oja
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2005486