On the analytic structure of the H∞ maximal ideal space

Abstract

We characterize the algebra H∞ ◦L_m, where m is a point of the maximal ideal space of H∞ with nontrivial Gleason part P(m) and L_m : D→P(m) is the coordinate Hoffman map. In particular, it is shown that for any continuous function f : P(m)→C with f ◦L_m ∈ H∞ there exists F ∈ H∞ such that F|_P(m) = f.