Douglas Algebras That Have No Maximal Subalgebra and No Minimal Superalgebra

Details Douglas Algebras That Have No Maximal Subalgebra and No Minimal Superalgebra Douglas Algebras That Have No Maximal Subalgebra and No Minimal Superalgebra

1995-11-13

arxiv.org/abs/math/9511210v1

Mathematics

Complex Variables

Scientific paper

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.

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