赋范线性空间中远达点的存在惟一性  

Existence and uniqueness of farthest points in normed linear spaces

作　　者：倪仁兴[1] 

机构地区：[1]绍兴文理学院数学系,浙江绍兴312000

出　　处：《宁夏大学学报（自然科学版）》2003年第1期1-5,共5页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10271025);浙江省自然科学基金资助项目(102002);浙江省教育厅科研基金资助项目(20010105)

摘　　要：研究了赋范线性空间中远达点的存在惟一性问题.用远达点的存在性给出了Banach空间中弱紧集和空间有限维的新特征刻画,并得到了自反和K 严格凸和(序列)Kadec空间中的每个有界闭子集均是强几乎K 惟一远达集的结论,进而推广和改进了已有的相应结果.Existence and uniqueness of farthest points in normed linear spaces are investigated. The new characterization theorems for finite dimensional Banach spaces and weakly compact sets of Banach spaces are given by the existence of farthest points. An example is given to show that Lau K S'(1975) results on weakly compact sets does not always extend to ω*compact sets in dual space X*,however, if Banach space X has the RadonNikodym property, then any ω*compact set in X* contains a farthest point. The results that a nonempty bounded closed subset of a reflexive Kstrictly convex and (sequence) Kadec space is strongly almost Kuniqueness farthest points set are established, also they extend and improve the corresponding ones.

关 键 词：赋范线性空间 远达点 存在惟一性 BANACH空间 弱紧集 强几乎K-惟一远达集 

分 类 号：O177.39[理学—数学]