Every Weakly Compact Set Can Be Uniformly Embedded into a Reflexive Banach Space  

作　　者：Li Xin CHENG Qing Jin CHENG Zheng Hua LUO Wen ZHANG 

机构地区：[1]Department of Mathematics, Xiamen University, Xiamen 361005, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第7期1109-1112,共4页数学学报（英文版）

基　　金：Supported by NSFC Grant No. 10771175

摘　　要：Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space.Based on an application of the Davis-Figiel-Johnson-Pelzyski procedure, this note shows that every weakly compact subset of a Banach space can be uniformly embedded into a reflexive Banach space. As its application, we present the recent renorming theorems for reflexive spaces of Odell- Schlumprecht and Hajek-Johanis can be extended and localized to weakly compact convex subsets of an arbitrary Banach space.

关 键 词：Banach space weakly compact set RENORMING 

分 类 号：O177.91[理学—数学] O177.3[理学—基础数学]