置换空间P_XX_n性质的补充

COMPLEMENT OF PROPERTY ON SUBSTITUTION SPACE P_XX_n

我们主要给出了如下结论 :(1)若X是自反局部一致凸Banach空间 ,则PXXn 是极端凸的当且仅当每个Xn(n =1,2 ,… )都是极端凸的 ;(2 )若X 是局部一致凸的 ,则PXXn 是一致G teaux可微的当且仅当每个Xn(n =1,2 ,… )都是一致G

In this paper, we maily give the following conclusions: (1) If X is a reflexive LUC space, then P XX n is extremely covex if and only if every X n(n=1,2,...) is extremely convex; (2) If X * is a LUC space, then P XX n is uniformly Gteaux differentiable if and only if every X n(n=1,2,...) is uniformly Gteaux differentiable.