论文标题
在订单单位空间的几何形状上
On the geometry of an order unit space
论文作者
论文摘要
我们介绍了$ \ mathit {skeleton} $的概念，并在非零的真实矢量空间中介绍了头。我们证明，带有头部的骨骼以几何形式描述订单单位空间。接下来，我们考虑$ \ mathit {courphery} $的概念，与骨架的一部分相对应。我们注意到，外围由带有单位规范的正锥的边界要素组成。我们讨论周围的一些基本特性。我们还找到了一个条件，在该条件下，$ v $将包含$ \ ell _ {\ infty}^n $的副本，对于某些$ n \ in \ mathbb {n} $作为订单单位子空间。
We introduce the notion of $\mathit{skeleton}$ with a head in a non-zero real vector space. We prove that skeletons with heads describe order unit spaces geometrically. Next, we consider the notion of $\mathit{periphery}$ corresponding to an order unit space which is a part of the skeleton. We note that periphery consists of boundary elements of the positive cone with unit norms. We discuss some elementary properties of the periphery. We also find a condition under which $V$ would contain a copy of $\ell_{\infty}^n$ for some $n \in \mathbb{N}$ as an order unit subspace.
