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Proceedings of the American Mathematical Society

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



A condition for analytic structure

Author: Richard F. Basener
Journal: Proc. Amer. Math. Soc. 36 (1972), 156-160
MSC: Primary 46J10
MathSciNet review: 0308789
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Abstract: Let X be a compact Hausdorff space, A a uniform algebra on X, M the maximal ideal space of A. Let $ f \in A$ and let W be a component of $ C\backslash f(X)$. Suppose that, for all $ \lambda \in W,{f^{ - 1}}(\lambda ) = \{ x \in M\vert f(x) = \lambda \} $ is at most countable. Then there is an open dense subset U of $ {f^{ - 1}}(W)$ which can be given the structure of a one-dimensional complex analytic manifold so that for all $ g \in A$, g is analytic on U.

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

  • [1] Errett Bishop, Holomorphic completions, analytic continuation, and the interpolation of semi-norms, Ann. of Math. (2) 78 (1963), 468–500. MR 0155016
  • [2] John Wermer, Banach algebras and several complex variables, Markham Publishing Co., Chicago, Ill., 1971. MR 0301514

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Keywords: Analyticity, maximal ideal space
Article copyright: © Copyright 1972 American Mathematical Society