Douglas algebras without maximal subalgebra and without minimal superalgebra
We give several examples of Douglas algebras that do not have any maximal subalgebra. We find a condition on these algebras that guarantees that some do not have any minimal superalgebra. We also show that if is the only maximal subalgebra of a Douglas algebra , then the algebra does not have any maximal subalgebra.
Copyright © 2001 Hindawi Publishing Corporation. 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.