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Transactions of the American Mathematical Society

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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
DOI: https://doi.org/10.1090/S0002-9947-1980-0574805-2
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$.


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

  • [1] I. Glicksberg, Function algebras with closed restrictions, Proc. Amer. Math. Soc. 14 (1963), 158-161. MR 0143050 (26:616)
  • [2] J.-P. Kahane, Séries de Fourier absolument convergentes, Ergebnisse der Math. und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin and New York, 1970. MR 0275043 (43:801)
  • [3] Y. Katznelson and W. Rudin, The Stone-Weierstrass property in Banach algebras, Pacific J. Math. 11 (1961), 253-265. MR 0126738 (23:A4032)
  • [4] Sungwoo Suh, Characterization of $ {L^1}(G)$ among its subalgebras, Thesis, Univ. of Connecticut, 1978.

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DOI: https://doi.org/10.1090/S0002-9947-1980-0574805-2
Article copyright: © Copyright 1980 American Mathematical Society

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