Boundaries for polydisc algebras in infinite dimensions

Abstract

AbstractLet AB be the algebra of all bounded continuous functions on the closed unit ball B of c0, analytic on the open unit ball, with sup norm, and let AU be the sub-algebra of AB of those functions which are uniformly continuous on B. Call a set S ⊂ B a boundary of AB (AU) iffor every f ∈ AB (f ∈AU, respectively). In the paper we study the boundaries of AB and AU. We give a complete description of the boundaries of AU and present some necessary and some sufficient conditions for a set to be a boundary of AB. We also give some examples of boundaries.