Types of Radon-Nikodym properties for the projective tensor product of Banach spaces

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.