# Questions tagged [choquet-theory]

The tag has no usage guidance.

9 questions
Filter by
Sorted by
Tagged with
165 views

### On examples of subspaces of $C(X)$ for which state spaces are Choquet Simplices

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 subspace $\mathcal{A}$ of $C(X)$ such that $\mathcal{A}$ ...
82 views

143 views

### Characterization of state spaces of Boolean algebras

A state space of a Boolean algebra is a Choquet simplex but not all Choquet simplices can be viewed as state spaces of Boolean algebras. Is it known which Choquet simplices are precisely state spaces ...
100 views

### Realizing certain affine functions on Choquet simplices on dimension groups

This is a question that is a bit outside my usual mathematical comfort zone, but I feel like an expert might know the answer. Recall that a dimension group is an ordered abelian group $G$ with ...
339 views

### Norms on $\mathbb{R}^d$ whose linear isometries are the hypercube group

It is a known fact that for any $2\neq p\in[1,\infty]$, the linear isometries for the corresponding norm $\|\cdot\|_p$ on $\mathbb{R}^d$ is the set of all square-matrices with entries in $\{-1,1,0\}$, ...
It’s relatively easy to show that if $J$ is a closed subgroup of a finite-dimensional real Banach space, $B$, then it is a vector subspace iff for all bounded linear functionals $\sigma$ of $B$, \$\...