A certain logmodular algebra and its Gleason parts (Q1113432)

Let A be a weak* Dirichlet algebra on a nontrivial probability measure space, and let \(H^{\infty}=H^{\infty}(m)\) be the weak* closure of A in \(L^{\infty}(m)\). The purpose of this paper is twofold. First, the author investigates the maximal ideal space \(M(H^{\infty})\) of \(H^{\infty}\) in relation to an algebraic direct sum decomposition of \(H^{\infty}\). Second, the author studies a certain logmodular algebra A, on a compact space X, in connection with an abstract Hardy algebra \(H^{\infty}\) associated with A.