拟赋范空间若干分析结构及其应用背景  

Analytical structures of quasi-normed spaces and its application

作　　者：苏永福[1] 

机构地区：[1]天津工业大学理学院,天津300160

出　　处：《天津工业大学学报》2004年第6期77-79,共3页Journal of Tiangong University

基　　金：天津市学科建设基金资助项目(100580204)

摘　　要：拟赋范空间是一类非局部凸线性拓扑空间,在非局部凸空间中它具有较好性质,许多泛函分析理论可建立在此空间上.文中首先证明了拟范数是一种吸收平衡非凸集的Minkowski泛函,再得到了拟赋范空间中正规锥的若干结论,同时指出了拟赋范空间若干应用背景.Quasi-normed spaces are a kind of non-locally convex linear topological spaces.However these non-locally convex spaces are possessed of characteristic topological structures, so that many fundamental theories on the functional analysis can be established on these spaces. Firstly, It is proved that quasi-norm is a Minkowski functional for a kind of absorbing balanced non-convex. Secondly, some results of the normal cone is proved.In the meantime, the application of quasi-normed spaces is pointed out.

关 键 词：拟范数 K-凸集 MINKOWSKI泛函 正规锥 半序 

分 类 号：O177.91[理学—数学]