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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.

References [Enhancements On Off] (What's this?)

  • [1] I. Glicksberg, Some uncomplemented function algebras, Trans. Amer. Math. Soc. 111 (1964), 121-137. MR 0161175 (28:4383)
  • [2] A. Pełczyński, Banach spaces of analytic functions and absolutely summing operators, CBMS Regional Conf. Ser. Math., No. 30, Amer. Math. Soc., Providence, R.I., 1977. MR 0511811 (58:23526)

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Keywords: Uniform algebra, projection, complemented
Article copyright: © Copyright 1984 American Mathematical Society

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