Banach空间中的超弱紧集合  

Super weakly compact subsets of Banach spaces

作　　者：程立新[1] 程庆进[1] CHENG Lixin;CHENG Qingjin(School of Mathematics Science,Xiamen University,Xiamen 361005,China)

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2021年第3期425-430,共6页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(11731010,12071389)。

摘　　要：超自反空间是非常重要的一类Banach空间,它的重要性不仅在理论上,还体现在应用上,例如空间结构理论、再赋范理论、不动点理论、鞅论、调和分析、无穷维非线性几何等领域的应用.随着20世纪末粗几何、非交换几何、非交换空间和非交换群论等新的数学领域兴起,它们对超自反空间及其局部化理论提出了新的课题.超弱紧集是超自反空间的一个局部化概念,本文将对Banach空间中超弱紧集理论研究进行简要的回顾,并列出该领域中亟待解决的问题.It is well known that,because of their nice properties,super reflexive Banach spaces have played a very important role in the geometry of Banach spaces and its applications.This includes the structural theory of spaces,renorming theory,fixed point theory,martingale theory,harmonic analysis,the nonlinear geometry of infinite-dimensional spaces,etc..With the development of coarse geometry,non-communicative geometry,non-communicative space and non-communicative group theory in recent years,it yields some new topics for super-reflexive space and its localized setting.The notion of super weakly compact sets is a localized setting of super reflexive Banach spaces.In this paper,we present a brief review of the research area of super weakly compact sets of Banach spaces and two questions to be solved are also listed.

关 键 词：BANACH空间 超弱紧集 一致Eberlein紧 

分 类 号：O177.2[理学—数学]