Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

Boundaries for polydisc algebras in infinite dimensions

J. Globevnika1

a1 University of Ljubljana

Abstract

Let 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 SB a boundary of AB (AU) if

S0305004100055705_eqnU1

for every f xs2208 AB (f xs2208AU, 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.

(Received March 07 1978)