International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 735-741
doi:10.1155/S0161171288000894
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.
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.