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International Journal of Mathematics and Mathematical Sciences
Volume 26, Issue 10, Pages 615-624

Some conditions on Douglas algebras that imply the invariance of the minimal envelope map

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA

Received 20 November 1999

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.


We give general conditions on certain families of Douglas algebras that imply that the minimal envelope of the given algebra is the algebra itself. We also prove that the minimal envelope of the intersection of two Douglas algebras is the intersection of their minimal envelope.