论文标题
凸锥的张量产品，第一部分：映射属性，面部和半透明性
Tensor Products of Convex Cones, Part I: Mapping Properties, Faces, and Semisimplicity
论文作者
论文摘要
可以以多种方式订购两个有序矢量空间的张量产品，就像可以多种方式进行标准的张量。过去，两种自然订单受到了相当大的关注，即投影性和注射式（或双向物品）锥体给出的订单。本文的目的是表明，这两个锥体的行为与它们的规范对应物相似，此外，将这两个锥体从代数张量产品扩展到了局部凸电张量产品。本文的主要结果是：（i）绘制与规范理论的相似之处，我们表明投影/注射锥具有类似于投影/注射范围的映射属性； （ii）我们为投影/注射锥的直接空间建立了直接公式，特别是提供了适当的必要条件； （iii）我们展示了如何从基本锥体的面上构建投影/注射锥的面孔，特别是提供了投影锥的极端射线的完整表征； （iv）我们证明了两个封闭锥的射影/注射量张量产物包含在封闭的圆锥体中（至少在代数张量产品中）。
The tensor product of two ordered vector spaces can be ordered in more than one way, just as the tensor product of normed spaces can be normed in multiple ways. Two natural orderings have received considerable attention in the past, namely the ones given by the projective and injective (or biprojective) cones. This paper aims to show that these two cones behave similarly to their normed counterparts, and furthermore extends the study of these two cones from the algebraic tensor product to completed locally convex tensor products. The main results in this paper are the following: (i) drawing parallels with the normed theory, we show that the projective/injective cone has mapping properties analogous to those of the projective/injective norm; (ii) we establish direct formulas for the lineality space of the projective/injective cone, in particular providing necessary and sufficient conditions for the cone to be proper; (iii) we show how to construct faces of the projective/injective cone from faces of the base cones, in particular providing a complete characterization of the extremal rays of the projective cone; (iv) we prove that the projective/injective tensor product of two closed proper cones is contained in a closed proper cone (at least in the algebraic tensor product).
