Abstract

When q is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra B of H∞[q¯] to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in B. If the set M(B)⋂Z(q) is not open in Z(q), we also find a condition that guarantees the existence of a factor q0 of q in H∞ such that B is maximal in H∞[q¯]. We also give conditions that show when two arbitrary Douglas algebras A and B, with A⫅B have property that A is maximal in B.