摘要
本文证明了如下结果：定理１设Ｘ是Ｂａｎａｃｈ空间，则：（Ⅰ）若Ｘ是Ｌω─ＵＲ，则Ｘ是ＬＦＮＵＣ；（Ⅱ）若Ｘ是严格凸的ＬＦＮＵＣ空间，则Ｘ是ＬωＲ空间。定理２设Ｘ是Ｂａｎａｃｈ空间，则：（１）若Ｘ是ω─ＵＲ，则Ｘ是ＦＮＵＣ；（Ⅲ）若Ｘ是严格凸的ＦＮＵＣ空间，则Ｘ是ωＲ空间。定理３：若Ｘ是ＵＫＫ空间且有ＢＳＰ；则Ｘ是ＦＮＵＣ空间。
In this paper. we prove the following results:(Ⅰ)If X os Lω UR(resp. ω-UR),then X is LFNUC:(resp.FNUC);(Ⅱ)If X is strictly convex LFNUC(resp.FNUC),then X is LωR(resp.ωR);(Ⅲ)If X is UKK and has BSP,then X is FNUC.
关键词
巴拿赫空间
完全近一致凸
LFNUC
Fully nearly uniform convex,locally fully nearly uniform convex,uniform-ly Kadec-Klee property. Banach-Saks property.
