Maximal subalgebra of Douglas algebra (Q1120795)

Summary: When q is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra B of \(H^{\infty}[\bar q]\) to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in B. If the set M(B)\(\cap Z(q)\) is not open in Z(q), we also find a condition that guarantees the existence of a factor \(q_ 0\) of q in \(H^{\infty}\) such that B is maximal in \(H^{\infty}[\bar q]\). We also give conditions that show when two arbitrary Douglas algebras A and B, with \(A\subseteq B\) have property that A is maximal in B.