ABSTRACT
Our goal here is to relax the requirement in Corollary 6.12 that the bound on the idempotents in the quotient algebras be uniform. We need some definitions and lemmas. The setting for the next three lemmas (from Katznelson [32]) is a compact Hausdorff space X and a Banach algebra A lying in C(X) which is normal and for which the idempotents in each quotient algebra A/kF are bounded. We will eventually prove (Theorem 7.8 below) that A must be all of C(X).
