(C-K)性质的特征

数学物理学报 ›› 1997, Vol. 17 ›› Issue (3): 280-284.

(C-K)性质的特征

王建华¹, 张子厚²

1 安徽师范大学 241000;
2 淮南电视大学 232001

收稿日期:1995-08-08 修回日期:1996-04-22 出版日期:1997-06-26 发布日期:1997-06-26

CHARACTERIZATIONS OF THE PROPERTY (C-K)

Wang Jianhua¹, Zhang Zhihou²

1 Department of Mathematics, Anhui Normal University Wuhu, Anhui 241000;
2 Anhui Huainan TV University, Huainan, Anhui 232001

Received:1995-08-08 Revised:1996-04-22 Online:1997-06-26 Published:1997-06-26

摘要/Abstract

摘要： 该文绘出(C-K),K=Ⅰ,Ⅱ,Ⅲ正性质的一些充要条件,从而我们得到:如果Banach空间X有(C一Ⅲ)((C-Ⅱ);(C-Ⅰ)性质,则对X的任意赋范集A⊂U(X^*),单位球面S(X)上的σ(X,A)拓朴与弱拓扑(范数拓扑)等价且X近非常凸(近强凸;强凸).

关键词: Kadec性质, 赋范集, 近非常凸, 近强凸, (C-K)性质

Abstract: In the theory of the best approximations the properties (C-K),K=Ⅰ,Ⅱ, Ⅲ play a very significant role (see[1]). The purpose of this paper is to give their interesting characterizations. Further we obtain that if a Banach space X has the property (C-Ⅲ) (resp.(C-Ⅱ)) then for any norming set A of X, the σ(X, A) topology and the weak topology (resp.norm topology) coincide on the unit sphere of X and X is nearly very rotund (resp. nealy strongly rotund).

Key words: Kadec property, Norming set, Near very rotundity, Near stong rotundity, Property (C-K)

王建华, 张子厚. (C-K)性质的特征[J]. 数学物理学报, 1997, 17(3): 280-284.

Wang Jianhua, Zhang Zhihou. CHARACTERIZATIONS OF THE PROPERTY (C-K)[J]. Acta mathematica scientia,Series A, 1997, 17(3): 280-284.