论文标题
有序拓扑矢量空间的表示和半透明性
Representations and Semisimplicity of Ordered Topological Vector Spaces
论文作者
论文摘要
本文研究了代表有序的拓扑矢量空间作为连续函数的空间的方法，从而扩展了Kadison和Schaefer的经典表示。特别强调的是半圣经空间的类别，由那些有序的拓扑矢量空间组成，这些拓扑矢量空间接纳了对连续功能空间的注入性阳性表示。我们表明，该类形成了1950年代Schaefer定义的定期订购空间的自然拓扑类似物，其特征是大量等效的几何，代数和拓扑特性。
This paper studies ways to represent an ordered topological vector space as a space of continuous functions, extending the classical representation theorems of Kadison and Schaefer. Particular emphasis is put on the class of semisimple spaces, consisting of those ordered topological vector spaces that admit an injective positive representation to a space of continuous functions. We show that this class forms a natural topological analogue of the regularly ordered spaces defined by Schaefer in the 1950s, and is characterized by a large number of equivalent geometric, algebraic, and topological properties.
