Observations About the Projective Tensor Product of Banach Spaces, Iii - L P [0 , 1] ⊗ X, 1 < P < ∞

Author: Bu Qingying   Dowling Patrick N.  

Publisher: Taylor & Francis Ltd

ISSN: 1607-3606

Source: Quaestiones Mathematicae, Vol.25, Iss.3, 2002-09, pp. : 303-310

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Abstract

Let X be a complex Banach space and 1 < p < ∞. Then the projective tensor product Lp [0, 1]⊗ X has the analytic Radon-Nikodym property (respectively, the near Radon-Nikodym property) if and only if X does. Also, L p[0, 1]⊗ X does not contain a copy of c0 if and only if X does not contain a copy of c0.