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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Algebras of Fourier transforms with closed restrictions

Author: Benjamin B. Wells
Journal: Trans. Amer. Math. Soc. 260 (1980), 631-636
MSC: Primary 43A20; Secondary 46J10
MathSciNet review: 574805
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Abstract: Let G denote a compact abelian group and let B denote a Banach subalgebra of A, the algebra of complex-valued functions on G whose Fourier series is absolutely convergent. If B contains the constant functions, separates the points of G, and if the restriction algebra, $ B(E)$, is closed in $ A(E)$ for every closed subset E of G, then $ B = A$.

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PII: S 0002-9947(1980)0574805-2
Article copyright: © Copyright 1980 American Mathematical Society