In this paper, we study the local ordered \(*\)-vector spaces and their representations. We prove that each Archimedean local ordered \(*\)-vector space, can be represented as a \(*\)-vector subspace of C(X), for some completely Hausdorff compactly generated space X. Furthermore, we show that for every Archimedean local ordered \(*\)-vector space V, there is a representation of V into the \(*\)-algebra of all noncommutative continuous functions on a quantum domain \({\mathcal {E}}\) such that the quantum order induced by this representation is the minimal quantum system structure on V.

中文翻译：

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Kadison表示定理的局部凸版本

在本文中，我们研究了局部有序\（* \）-向量空间及其表示。我们证明，对于某些完全由Hausdorff紧致生成的空间X，每个Archimedean局部有序\（* \）-向量空间都可以表示为C（X）的\（* \）-向量子空间。此外，我们还表明，对于每一个阿基米德局部有序\（* \）维矢量空间V，还有的表示V到\（* \）对量子域中的所有非对连续函数代数\（{\ mathcal { E}} \）这样，由该表示所诱导的量子级就是V上的最小量子系统结构。