International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 735-741

Maximal subalgebra of Douglas algebra

Carroll J. Gullory

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 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 AB have property that A is maximal in B.