Questions tagged [choquet-theory]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
1answer
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 $\mathcal{A}$ ...
2
votes
1answer
82 views

Ergodic decomposition - how does restricting measure effect it? (Choquet Theory)

Suppose that $G$ is a discrete countable group and $\mu$ is an IRS (invariant random subgroup) of $G$: $\mu$ is conjugation invariant as a probability measure on the subgroups of $G$. Since all the $...
1
vote
1answer
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 ...
3
votes
1answer
292 views

Peak sets and Choquet boundary of a function algebra

I have two problems to ask. Let $A$ be a function algebra of $C(K)$. $t\in K$ is said to be a peak point of $A$ if $\exists~f\in A$ s.t. $|f(t)|=\|f\|$ and $|f(s)|<|f(t)|$ for any $s\neq t$. ...
2
votes
0answers
204 views

Dual of the space of affine functions

Let $M^+(D)$ be the space of all positive measures on a closed convex subset $D$ of a locally convex topological vector space $E$. Two measure $\mu, \nu\in M^+(D)$ one can define a partial ordering $\...
1
vote
1answer
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 ...
6
votes
2answers
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 $\{-1,1,0\}$, ...
4
votes
0answers
187 views

SubGROUPs of Banach spaces, when are they dense in a vector subspace?

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 $B$, $\...
5
votes
1answer
652 views

Is there a non-compact Poulsen simplex?

A Choquet simplex is a closed, convex and metrizable subset of a locally convex Hausdorff topological vector space in which every point is a barycenter of a unique probability measure supported on the ...