Banach空间X的弱局部Zk性质

The Weak Local Zk -Property of Banach Spaces

中文关键词:  局部K接近一致凸  K接近一致凸  弱局部Z_k性质  弱Z_k性质

英文关键词:local K-nearly uniformly conex, K-nearly uniformly convex, weak local Z_k-property, weak Z_k-property, weak Banach-Saks property.

中文摘要:

      本文引入了Ｂａｎａｃｊ空间Ｘ的弱局部Ｚ_k性质和弱Ｚ_k性质，得出了：Ｂａｎａｃｈ空间Ｘ是Ｋ－ＮＵＣ空间的一个充分必要条件和Ｂａｎａｃｈ空间Ｘ是ＬＫ－ＮＵＣ空间的一个充分条件，并指出弱Ｚ_k性质蕴含弱Ｂａｎａｃｈ－Ｓａｋｓ性质．

英文摘要:

      In this paper we in troduce the weak local Z_k-property and the weak Z_k-property. With these concepts we give a characterization that a Banach space is K-NUC space. We also obtain a sufficient condition for a Banach space to be a LK-NUC space. We prove that weak Z_k-property implies weak Banach-Saks property.