# Seminário de Análise, Geometria e Sistemas Dinâmicos

### The Choquet boundary of amenable nonselfadjoint operator algebras

For any compact and Hausdorff set $X$, the Choquet boundary of  an amenable function algebra $A$ in the algebra $C(X)$ of continuous and complex functions on $X$ is exactly $X$. The problem is lifted to non commutative cases where $A$ is an operator algebra and $X$ is replaced by irreducible representations.