International Journal of Mathematics and Mathematical Sciences 
Volume 26 (2001), Issue 10, Pages 615-624
doi:10.1155/S0161171201004148

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

Carroll Guillory

 Department of Mathematics, University of Louisiana at Lafayette, Lafayette 70504, LA, USA
Received 20 November 1999

Abstract

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.