Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Rad...Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.展开更多
基金the National Natural Science Foundation of China,Grant No.10571035
文摘Let X and Y be Banach spaces such that X has an unconditional basis. Then X Y, the injective tensor product of X and Y, has the Radon-Nikodym property （respectively, the analytic Radon-Nikodym property, the near Radon-Nikodym property, non-containment of a copy of co, weakly sequential completeness） if and only if both X and Y have the same property and each continuous linear operator from the predual of X to Y is compact.
