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AU（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）.
In the theory of the best approximations the properties (C-K),K = Ⅰ,Ⅱ, Ⅲplay a very significant role (see[1]). The purpose of this paper is to give their interestingcharacterizations. 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. nealystrongly rotund ).
出处
《数学物理学报（A辑）》
CSCD
北大核心
1997年第3期280-284,共5页
Acta Mathematica Scientia
关键词
Kadec性质
赋范集
巴拿赫空间
(C-K)性质
Kadec property, Norming set, Near very rotundity, Near stong rotundity, Property (C-K)
