局部p-凸空间理论简介

BRIEF INTRODUCTION TO LOCALLY p-CONVEX SPACE THEORY

文章以新著《局部p-凸空间引论》为主要依据,综合其它资料,简单介绍局部p-凸空间理论的发展脉络,基本框架,部分最新成果与主要研究方法,给出以局部p-凸空间中的分离定理,Hahn-Banach延拓定理,局部有界定理与一致有界定理为主线的p-凸分析理论体系,最后以几个典型空间的共轭锥的次表示定理结束全文.

Based mainly on the new book of Introduction to Locally p-Convex Spaces, combining with other references, this paper makes a brief introduction to the development history, basic framework, some latest achievements and the main research methods of locally p-convex space theory. The separation theorem, the Hahn-Banach extension theorem, the local boundedness theorem and the uniform boundedness theorem in locally p-convex spaces are given in this paper, which con- stitute the main theory system of locally p-convex analysis. The paper is ended by several subrepresentation theorems of some typical locally p-convex spaces at last.