论文标题
Ramsey属性用于操作员空间和非交通式Choquet Sublices
The Ramsey property for Operator spaces and noncommutative Choquet simplices
论文作者
论文摘要
非交换性gurarij space $ \ mathbb {\ mathbb {\ mathbb {ng}}}} $，最初由Oikhberg定义，是操作员空间理论中的规范对象。正如“有限维核操作员空间”类别的fra \“ıssé极限，它可以看作是古典gurarij banach空间的非共同类似物。在本文中，我们证明了$ \ mathbb {\ mathbb {\ mathbb {ng {ng {ng} $的自动形态群体，即均一的comption。证明依赖于双重ramsey定理，以及在操作员空间的设置中的kechris-pestov-todorcevic对应关系。 戴维森（Davidson）和肯尼迪（Kennedy）的最新作品是基于阿尔维森（Arveson），埃弗罗斯（Effros），法里尼克（Farenick），韦伯斯特（Webster）和温克勒（Winkler）等先前作品的基础，表明核操作员系统可以看作是Choquet Simplices的非共同类似物。在这种情况下，Poulsen单纯形的类似物是fra \“ ra \”的矩阵状态空间$ \ mathbb {np} $ $ a（\ mathbb {np}）$上的$ \ mathbb {np} _1 $ unital线性函数是最小的，并且它因任何最小动作而取决于\ textrm {aut} $ \ left（\ mathbb {np {np right）$的通用最小流动的描述。
The noncommutative Gurarij space $\mathbb{\mathbb{\mathbb{NG}}}$, initially defined by Oikhberg, is a canonical object in the theory of operator spaces. As the Fra\"ıssé limit of the class of finite-dimensional nuclear operator spaces, it can be seen as the noncommutative analogue of the classical Gurarij Banach space. In this paper, we prove that the automorphism group of $\mathbb{\mathbb{NG}}$ is extremely amenable, i.e.\ any of its actions on compact spaces has a fixed point. The proof relies on the Dual Ramsey Theorem, and a version of the Kechris--Pestov--Todorcevic correspondence in the setting of operator spaces. Recent work of Davidson and Kennedy, building on previous work of Arveson, Effros, Farenick, Webster, and Winkler, among others, shows that nuclear operator systems can be seen as the noncommutative analogue of Choquet simplices. The analogue of the Poulsen simplex in this context is the matrix state space $\mathbb{NP}$ of the Fra\"ıssé limit $A(\mathbb{NP})$ of the class of finite-dimensional nuclear operator systems. We show that the canonical action of the automorphism group of $\mathbb{NP}$ on the compact set $\mathbb{NP}_1$ of unital linear functionals on $A(\mathbb{NP})$ is minimal and it factors onto any minimal action, whence providing a description of the universal minimal flow of \textrm{Aut}$\left( \mathbb{NP}% \right) $.
