拟Banach空间与K-凸集上Minkowski泛函

Quasi-banach Spaces and Minkowski Functional of K-convex

拟Banach空间即是完备的赋拟范线性空间,一般的拟Banach空间,不是局部凸的拓扑线性空间.然而,这类非局部凸空间又有其特有的拓扑结构,从而使泛函分析理论中许多基本内容可以建立在这一类空间上.该文讨论了赋拟范线性空间与拟Banach空间基本拓扑结构,尤其是拟范数与K＿凸集上Minkowski泛函的关系.

Quasi-Banach spaces are complete Quasi-normed linear spaces. These spaces are not locally convex linear topological spaces. However these non-locally convex spaces are still with characteristic topologicl structures, so that many fundamental theories on the functional analysis can be established on these spaces. In this paper, the fundamental concepts for quasi-normed linear spaces and theory of cone are studied.