Douglas Algebras That Have No Maximal Subalgebra and No Minimal Superalgebra

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.

Cited by in corpus (1)

• Bourgain algebras, minimal envelopes, minimal support sets, and some applications