International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 735-741
Maximal subalgebra of Douglas algebra
Department of Mathematics, University of Southwestern Louisiana, Lafayette 70504, Louisiana, USA
Received 1 April 1987
Copyright © 1988 Carroll J. Gullory. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
When is an interpolating Blaschke product, we find necessary and sufficient conditions for a subalgebra of to be a maximal subalgebra in terms of the nonanalytic points of the noninvertible interpolating Blaschke products in . If the set is not open in , we also find a condition that guarantees the existence of a factor of in such that is maximal in . We also give conditions that show when two arbitrary Douglas algebras and , with have property that is maximal in .