论文标题
半态有序矢量空间的Archimedean Order Order Onitization
The Archimedean order unitization of seminormed ordered vector spaces
论文作者
论文摘要
在本文中，我们描述了一种将半态的预订矢量空间变成阿基米德秩序单位空间的方法。我们表明，这种构造满足了与Paulsen和Tomforde的Archimedeanized相似的通用性能，并且我们在有序的向量空间和矩阵有序的操作员空间中给出了许多结果的应用。在有序的矢量空间中，我们使用我们的阿基米德秩序单位化为半静物的正态性标准提供了新的启示。在矩阵有序的操作员空间中，我们证明了有关Werner的“部分校准”的几个新结果：我们对Werner局部校准的正面锥进行了简化的“内部”描述，并且我们证明，矩阵有序的操作员空间将其部分校准嵌入其部分的必要条件，以使其成为完整的同等同学。最后的结果已经在Werner的2002年论文中宣布，但据我们所知，文献中没有证据。
In this paper, we describe a way of turning a seminormed preordered vector space into an Archimedean order unit space. We show that this construction satisfies a universal property similar to that of the Archimedeanization of Paulsen and Tomforde, and we give a number of applications of our result in ordered vector spaces and in matrix ordered operator spaces. In ordered vector spaces, we use our our Archimedean order unitzation to shed new light on normality criteria for seminorms. In matrix ordered operator spaces, we prove several new results about Werner's "partial unitization": we give a simplified "internal" description of the positive cone of Werner's partial unitization, and we prove a necessary and sufficient condition for the embedding of a matrix ordered operator space in its partial unitization to be a complete isomorphism. This last result was already announced in Werner's 2002 paper, but to our knowledge no proof exists in the literature.
