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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Uniform algebras and projections


Author: S. J. Sidney
Journal: Proc. Amer. Math. Soc. 91 (1984), 381-382
MSC: Primary 46J10; Secondary 46E25
MathSciNet review: 744634
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Abstract: If $ M$ is a closed $ A$-submodule of $ C\left( X \right)$ where $ A$ is a uniform algebra on $ X$ which contains a separating family of unimodular functions, and if $ M$ is a quotient space of some $ C\left( Y \right)$, then $ M$ is an ideal in $ C\left( X \right)$. If there is an example of a uniform algebra $ A$ on some $ X$ such that $ A \ne C\left( X \right)$ but $ A$ is complemented in $ C\left( X \right)$, then there is such an example with $ A$ separable.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0744634-4
PII: S 0002-9939(1984)0744634-4
Keywords: Uniform algebra, projection, complemented
Article copyright: © Copyright 1984 American Mathematical Society