Interpolating sequences and the Shilov boundary of H∞(Δ)

Let H^∞(Δ) denote the Banach algebra of bounded analytic functions on the open unit disc, let $\text{M}$ denote its maximal ideal space, and let ? denote its Shilov boundary. D. J. Newman has shown that a homomorphism ? in $\text{M}$ will be in ? if and only if ? is unimodular on all Blaschke products. We answer a question of K. Hoffman by showing that ? will be in ? if and only if ? is unimodular on every Blaschke product whose zero set is an interpolating sequence. Our method is based on a construction due to L. Carleson, originally developed for the proof of the Corona theorem.