摘要
本文首先证明Banach空间X是逼近紧的当且仅当X是近可凹的;其次给出对偶空间中每个弱*内点非空的弱*闭凸子集A是逼近紧(或逼近弱紧的)的一系列特征刻画.其证明利用到Banach空间几何理论中的一些巧妙的技巧.
In this paper, we first prove that approximative compactness and near dentability are equivalent for a Banach space. Then, we present several characterizations that every weak＊closed convex subset with non-empty weak＊interior in a dual space is either approximatively compact or weakly approximatively compact.Our proofs are based on some subtle techniques in geometry of Banach spaces.
出处
《中国科学：数学》
CSCD
北大核心
2015年第12期1953-1960,共8页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11271248和11401370)资助项目
关键词
近可凹性
逼近紧性
逼近弱紧性
度量投影
H
性质
很光滑空间
弱＊可凹点
near dentablity
approximative compactness
approximative weak compactness
metric projection
property H
very smooth space
weak＊denting point
