摘要
设X是Banach空间。称X是弱紧局部一致凸的(WCLUR),如果x_2,x∈X,‖x_2=‖x‖=1,‖x_2+x‖→Z,则{x_n}有弱敛子序列。在这个意义下,我们证明:如果X*是(WCLUR),则X*有Radon-Nikodym性质。
Let X be a Banach space. X is said to be weakly compact locally uniformly rotund (WCLUR) if x_u, in X, ‖x_u‖=‖x‖=1, ‖x_u+x‖—→2, then (x_u) has a weakly convergent subsquence. This note shows that if x~* is (WCLUR), then X~* has RNP.
