Generalized Douglas algebras and the corona theorem (Q1814386)

The paper deals with the structure of the maximal ideal space of generalized Douglas algebras. Given a Douglas algebra \(B\) the corresponding generalized Douglas algebra \({\mathcal H}_ B\) consists of all continuous functions on \(D=\{z\in\mathbb{C}\): \(| z|<1\}\) having non-tangential limits a.e. on \(T=\{z\in\mathbb{C}\): \(| z|=1\}\) such that the resulting boundary function belongs to \(B\). For the special case \({\mathcal H}_{H^ \infty}\) a two-sheeted analogon on the Corona theorem is proved.