Banach-Saks性质与近一致凸、紧完全凸性

THE BANACH-SAKS PROPERTY AND NEARLY UNIFORM CONVEXITY, COMPACT FULLY CONVEXITY

本文通过引入 B- NUC Banach空间及 WB性质 ,进一步研究 Banach- Saks性质(BSP)与近一致凸及紧完全凸性之间的关系 .得到以下主要结果 :1 ) Banach空间 X具有 WB性质当且仅当 X具有 WBanach- Saks性质 (WBSP) ;2 ) X是 B- NUC空间当且仅当 X是具 BSP的 NUC空间 ;3)若 X具 BSP及 (H)性质 ,则 X是 CωR空间 (紧完全 ω-凸空间 )

In this paper,by introducing the B NUC Banach space and the property WB,we go further into the relationship between the Banach Saks property and nearly uniform convexity,compact fully ω convexity.We obtain the following results: 1)Banach space X has the property WB if and only if X has the W Banach Saks property (WBSP). 2)X is a B NUC space if and only if X is an NUC space with BSP. 3)If X has the BSP and the property (H),then X is CωR apace (compact fully ω convex space).