Algebras of Fourier transforms with closed restrictions
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- by Benjamin B. Wells PDF
- Trans. Amer. Math. Soc. 260 (1980), 631-636 Request permission
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
- I. Glicksberg, Function algebras with closed restrictions, Proc. Amer. Math. Soc. 14 (1963), 158–161. MR 143050, DOI 10.1090/S0002-9939-1963-0143050-2
- Jean-Pierre Kahane, Séries de Fourier absolument convergentes, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 50, Springer-Verlag, Berlin-New York, 1970 (French). MR 0275043
- Yitzhak Katznelson and Walter Rudin, The Stone-Weierstrass property in Banach algebras, Pacific J. Math. 11 (1961), 253–265. MR 126738 Sungwoo Suh, Characterization of ${L^1}(G)$ among its subalgebras, Thesis, Univ. of Connecticut, 1978.
Additional Information
- © Copyright 1980 American Mathematical Society
- 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