局部β-凸空间中β-次半范的Hahn-Banach延拓定理及其应用  

The Hahn-Banach Theorems about β-Subseminorms In Locally β-convex spaces and Their Applications

作　　者：王见勇[1] 

机构地区：[1]常熟理工学院数学系,江苏常熟215500

出　　处：《常熟理工学院学报》2006年第4期19-24,共6页Journal of Changshu Institute of Technology

基　　金：江苏省教育厅指导性项目

摘　　要：研究了β-次半范的Hahn-Banach延拓问题,得到线性空间中β-次半范的控制延拓定理,连续β-次半范在局部β-凸空间中的连续延拓定理及在赋β-范空间中的保范延拓定理等.作为Hahn-Banach延拓定理的应用,最后证明了局部β-凸空间的共轭锥对空间本身的分离定理.This paper deals with the extension problems about β- subseminorms, the control extension theorem of β - subseminorms in linear spaces, the Hahn - Banach continuous extension theorem of continous β- subseminorms in locally β- convex spaces and the norm - preserving extension theorem of continous β- subseminorms in β- normed spaces are obtained. As the application of Hahn - Banach extension theorems, the theorem of Xβ distinguishing X is obtained at the end of this paper.

关 键 词：局部Β-凸空间 (连续)β-次半范 (赋范)共轭锥 Hahn—Banach延拓定理 

分 类 号：O177.3[理学—数学]