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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Subalgebras of Douglas algebras


Authors: Kevin Clancey and Wayne Cutrer
Journal: Proc. Amer. Math. Soc. 40 (1973), 102-106
MSC: Primary 46J15
DOI: https://doi.org/10.1090/S0002-9939-1973-0318895-2
MathSciNet review: 0318895
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Abstract: A closed subalgebra $ \mathcal{A}$ of $ {L^\infty }$ is called a Douglas algebra in case $ \mathcal{A}$ is an algebra generated by $ {H^\infty }$ and a set of inverses of inner functions. It is shown that if the Douglas algebra $ \mathcal{A}$ contains properly $ {H^\infty } + C$, then there is another Douglas algebra $ \mathcal{A}'$ such that $ {H^\infty } + C \subsetneq \mathcal{A}' \subsetneq \mathcal{A}$. Some results on subalgebras are also given for algebras generated by $ {H^\infty }$ and a function of the form $ f\overline B $, where $ f$ is in $ {H^\infty }$ and $ B$ is an infinite Blaschke product.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0318895-2
Article copyright: © Copyright 1973 American Mathematical Society