Abstract
Let $X$ and $Y$ be Banach spaces such that $X$ has a boundedly complete basis. Then $X\hat{\otimes}Y$, the projective tensor product of $X$ and $Y$, has the Radon-Nikodym property (resp.~the analytic Radon-Nikodym property, the near Radon-Nikodym property, contains no copy of $c_0$) if and only if $Y$ has the same property.
Citation
Qingying Bu. Joe Diestel. Patrick Dowling. Eve Oja. "Types of Radon-Nikodym properties for the projective tensor product of Banach spaces." Illinois J. Math. 47 (4) 1303 - 1326, Winter 2003. https://doi.org/10.1215/ijm/1258138106
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