w-Frchet可微性质和Radon-Nikod(?)m性质以及w-Asplund空间  

The w-Frchet Differentiability Property, the Radon-Nikod(?)m Property and w-Asplund Spaces

作　　者：程立新[1] 吴从炘[2] 

机构地区：[1]厦门大学数学研究所,厦门361005 [2]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《数学学报（中文版）》2003年第2期385-390,共6页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10071063;60074015)

摘　　要：我们称定义在一个Banach空间的对偶空间上的广义实值w*-下半连续凸函数f具有w*-Frechet可微性质(w*-FDP),如果对于该对偶空间上的每个w*-下半连续的广义实值凸函数g,只要g≤f,就有g在intdom g的某个稠密的Gδ-子集上处处Frechet可微.本文用集合的Radon-Nikodym性质刻划了该种函数的特征.作为它的一个直接推论,给出了局部化的Collier定理.We say an extended real-valued w*-lower semi-continuous convex function f on a dual Banach space E* has w*-Frechet differentiablity property (w*-FDP), if for every w*-lower semi-continuous proper convex function g on E*, g ≤f, implies that g is Frechet differentiable at each point of a dense Gδ-subset of the interior of dom f (the effective domain of f). This paper characterizes the w*-FDP of the functions f by the Radon- Nikodym property of subsets in the pre-dual E, and as a direct consequence, it gives a localized Collier's theorem.

关 键 词：凸函数 可微性 ω＊-Fréchet可微性质 RADON-NIKODYM性质 ω＊-Asplund空间 

分 类 号：O177.2[理学—数学] O174.13[理学—基础数学]