置换空间P_XX_n中几种凸性的提升

THE LIFTING RESULTS OF SEVERAL CONVEXITIES IN SUBSTITUTION SPACES P XX n

主要研究强凸、非常凸等性质从Ｂａｎａｃｈ空间Ｘｎ到ＰＸＸｎ的提升问题，证明了当Ｘ是局部一致凸空间时，空间ＰＸＸｎ是强凸（非常凸或近强凸）当且仅当每个Ｘｎ都是强凸（非常凸或近强凸）．

This paper gives the following results: P XX n is strongly convex (very convex, nearly strongly convex) if and only if every X n (n =1,2,…) is strongly convex too.