摘要
本文定义了近可凹的Banach空间.利用Banach空间几何技巧证得:X是逼近紧的当且仅当(1)X是近可凹的;(2)X是近严格凸的.还证明了如果Banach空间X是近可凹的,则对任意闭凸集C,度量投影算子PC是上半连续的.最后作者给出了近可凹性在广义逆理论中的应用.
In this paper, authors define nearly dentability of Banach space. Authors prove that X is approximatively compact if and only if (1) X is nearly dentable space, and (2) X is nearly strict convex space. By the method of geometry of Banach spaces, authors also prove that if X is nearly dentable space, then for any closed convex subset C, metric projector Pc is upper semicontinuous. Finally, authors give important application of nearly dentability in generalized inverse theory.
出处
《中国科学:数学》
CSCD
北大核心
2011年第9期815-825,共11页
Scientia Sinica:Mathematica
基金
国家自然科学基金(批准号:11061022)
哈尔滨理工大学学科带头人基金资助项目
关键词
近可凹性
逼近紧性
度量投影算子
上半连续
近严格凸性
nearly dentability, approximative compactness, metric projector, upper semicontinuous
nearlystrictly convexity