THE WEAK RADON-NIKODYM PROPERTY IN SPACES OF NUCLEAR OPERATORS

Abstract

We prove that if X and Y are Banach spaces such that X* has the weak Radon-Nikodym property (WRNP), Y has the Radon-Nikodym property (RNP) and Y is complemented in its bidual, then the space N(X,Y) of all nuclear operators from X to Y has the WRNP. If moreover X* has the RNP, then N(X,Y) has the RNP.