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 RadonNikodym property, then any ω*compact set in X* contains a farthest point. The results that a nonempty bounded closed subset of a reflexive Kstrictly convex and (sequence) Kadec space is strongly almost Kuniqueness farthest points set are established, also they extend and improve the corresponding ones.
出处
《宁夏大学学报（自然科学版）》
CAS
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)
