The noncommutative Gurarij space $\mathbb{NG}$, initially defined by Oikhberg, is a canonical object in the theory of operator spaces. As the Fraïssé 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 $\mathbb{NG}$ 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 Fraïssé 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 Aut$\left(\mathbb{NP}\right)$.

非对易 Gurarij 空间 $\mathbb{NG}$最初由 Oikhberg 定义，是算子空间理论中的规范对象。作为有限维核算子空间类的 Fraïssé 极限，它可以看作是经典 Gurarij Banach 空间的非对易类比。在本文中，我们证明了自同构群$\mathbb{NG}$非常适合，即它在紧凑空间上的任何动作都有一个固定点。该证明依赖于对偶拉姆齐定理，以及算子空间设置中的 Kechris-Pestov-Todorcevic 对应关系的一个版本。

Davidson 和 Kennedy 最近的工作建立在 Arveson、Effros、Farenick、Webster 和 Winkler 等人之前的工作基础上，表明核算子系统可以被视为 Choquet 单纯形的非对易类比。在这种情况下，波尔森单纯形的类似物是矩阵状态空间$\mathbb{NP}$ Fraïssé 极限 $\mathrm{一种}(\mathbb{NP})$有限维核算子系统类。我们证明了自同构群的规范作用$\mathbb{NP}$ 在紧凑集上 ${\mathbb{NP}}_1$ 单位线性泛函 $\mathrm{一种}(\mathbb{NP})$ 是最小的，它会影响任何最小的动作，从而提供对 Aut 的通用最小流的描述$\left(\mathbb{NP}\right)$.