Let $C(X)$ be the Banach space of all real-valued continuous functions on a compact Hausdorff space $X$. What are examples of uniformly closed subspaces $\mathcal{A}$ of $C(X)$ such that $\mathcal{A}$ separates points, containing constants and the state space of $\mathcal{A}$ is a Choquet simplex?

The state space of $\mathcal{A}$ is defined as the set of all continuous linear functionals $\Lambda$ on $\mathcal{A}$ where $\|\Lambda\|=1$ and $\Lambda (1)=1$. By a Choquet simplex we mean a compact convex subset $K$ of a locally convex topological vector space $E$ such that for each $p\in K$, there exists a unique measure $\lambda$ on $K$ such that $f(p)=\int_K f(t)d \lambda (t)$, $\forall~ f\in E^*$. In the metrisable case $\lambda$ can be assumed as $S(\lambda)\subseteq \operatorname{ext} (K)$ but for non-metrisable case $S(\lambda)\subseteq \overline{\operatorname{ext}(K)}$, in some sense these measures are 'maximal'.