关于局部完全凸和弱局部完全凸空间

On the LFR and WLFR Spaces

本文引入了LFR和WLFR,它们分别是kR、FR、LkR和WLkR的推广;主要结论是:(1)若X是LFR且具有Bishop-Phelps性质,则X的每个有界闭的,绝对凸的子集是它强暴露点的闭凸包.(2)X是LUR当且仅当X是LFR且具有(WM)性质.

In this paper. Locally fully convex space(LFR) and weak locally fully convex space(WLFR) are introduced. The main results are as follows:(1)If X is a LFR and has Bishop -Phelps property , then every closed , bounded , absolutely convex subset of X is the closed convex hull of its strongly exposed points.(2)X is LUR space if and only if X is LFR space and has(WM) property.