摘要
给出Hilbert空间到其自身不具有关于锥的例外族的映射条件 ,利用Hilbert空间可表为闭凸锥与负对偶锥的特点研究映射关于锥的例外簇的特性 ,证明了可通过映射在某紧凸子集上的性态判断其例外簇的存在与否 。
The conditions that mappings from a Hilbert space to itself have no exceptional family with respect to a cone are presented. The conception is based on the feature of Hilbert space that can be expressed as the sum of a closed convex cone and its negative dual cone. The results obtained show that characteristics of mappings in a compact subset of cone determine whether or not the exceptional family exists. Meanwhile, problems of no exceptional family on the several kinds of monotone mappings are studied.
出处
《数学研究》
CSCD
2002年第1期44-48,共5页
Journal of Mathematical Study
基金
国家自然科学基金资助项目 (6 9972 0 36 )
陕西省自然科学研究项目 (2 0 0 0SL0 3)
