近可凹性和Banach空间的逼近紧性及度量投影算子的连续性

Nearly dentability and approximative compactness and continuity of metric projector in Banach spaces

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.