Abstract and Applied Analysis
Volume 6 (2001), Issue 1, Pages 1-11
doi:10.1155/S1085337501000458
Douglas algebras without maximal subalgebra and without
minimal superalgebra
University of Louisiana at Lafayette, Lafayette 70504, LA, USA
Received 25 February 2001
Copyright © 2001 Carroll Guillory. 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
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 A
is the only maximal subalgebra of a Douglas
algebra B, then the algebra A does
not have any maximal subalgebra.