C~＊PCP与（w~＊－w）CPCP的关系

RELATIONSHIP BETWEEN THE C￣*PCP AND THE (W￣*-W)CPCP

本文证明了下面２个结果：（１）当Ｘ＊具有ＰＣＰ时，Ｃ＊ＰＣＰ与（ｗ＊－ｗ）ＣＰＣＰ等价；（２）Ｘ＊具有Ｃ＊ＰＣＰ当且仅当Ｘ＊具有（ｗ＊－ｗ）ＣＰＣＰ且对Ｘ＊的每个非空ｗ＊－紧凸子集Ｋ，（ｗ＊－ｗ）ＰＣ（Ｋ）含有Ｋ的一个ｗ＊－稠密Ｇ子集．

This paper shows two results: 1. If X* has the PCP, then the C*PCP and the (w*-w)CPCP are equivalent; 2. X* has the C*PCP if and only if X* has the (w*-w)CPCP and (w*-w)PC(K) contains a w*-dense G subset of K for every non-empty w*-compact convex subset of X*.