Peak points for hypo-Dirichlet algebras

Abstract

A proof is given of a theorem limiting the number of points not in the Choquet boundary for certain uniform algebras. In the hypo-Dirichlet case the argument reduces to a short proof that every point is in the Choquet boundary. Also, a lemma is presented which describes, for certain subalgebras of codimension one in a uniform algebra, a relation between certain spaces of real functions associated with the original algebra, and the corresponding spaces associated with the subalgebra.