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Proceedings of the American Mathematical Society

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

 
 

 

Relations between Banach function algebras and their uniform closures


Author: Taher G. Honary
Journal: Proc. Amer. Math. Soc. 109 (1990), 337-342
MSC: Primary 46J20; Secondary 46J10
DOI: https://doi.org/10.1090/S0002-9939-1990-1007499-4
MathSciNet review: 1007499
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Abstract: Let $ A$ be a Banach function algebra on a compact Hausdorff space $ X$. In this paper we consider some relations between the maximal ideal space, the Shilov boundary and the Choquet boundary of $ A$ and its uniform closure $ \bar A$. As an application we determine the maximal ideal space, the Shilov boundary and the Choquet boundary of algebras of infinitely differentiable functions which were introduced by Dales and Davie in 1973.


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DOI: https://doi.org/10.1090/S0002-9939-1990-1007499-4
Keywords: Banach function algebras, uniform algebras, maximal ideal space, Shilov boundary, Banach algebras of differentiable functions
Article copyright: © Copyright 1990 American Mathematical Society

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