Convexity properties of state spaces of uniform algebras (Q1098066)

Let A be a uniform algebra on a compact Hausdorff space X and let \[ S_ A:=\{L\in A^*: L(1)=1=\| L\| \} \] be the state space of A. \(S_ A\) is a compact convex set in the weak-star-topology. In his main result the author shows that, under certain conditions, the convex hull of two state spaces of uniform algebras is a state space of a third uniform algebra.