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On the ideal of unconditionally convergent Fourier series in $ L\sb{p}\,(G)$


Author: Gregory F. Bachelis
Journal: Proc. Amer. Math. Soc. 27 (1971), 309-312
MSC: Primary 42.56; Secondary 46.00
DOI: https://doi.org/10.1090/S0002-9939-1971-0271640-X
MathSciNet review: 0271640
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Abstract: Let $ G$ be a compact abelian group. We consider the ideal of functions in $ {L_p}(G)$ with unconditionally convergent Fourier series in the $ {L_p}$ norm. This ideal is shown to coincide with the ``Derived algebra'' of Helgason. A characterization of this ideal is given when $ p$ is an even integer.


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  • [1] G. F. Bachelis, Homomorphisms of annihilator Banach algebras, Pacific J. Math. 25 (1968), 229-247. MR 39 #6076. MR 0244762 (39:6076)
  • [2] M. M. Day, Normed linear spaces, 2nd rev. ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, Heft 21, Academic Press, New York; Springer-Verlag, Berlin, 1962. MR 26 #2847.
  • [3] R. E. Edwards, Fourier series: A modern introduction. Vol II, Holt, Rinehart and Winston, New York, 1967. MR 36 #5588. MR 0222538 (36:5588)
  • [4] A. Grothendieck, Résultats nouveaux dans la théorie des opérations linéaires. I, C. R. Acad. Sci. Paris. 239 (1954), 577-579. MR 16, 596. MR 0066556 (16:596b)
  • [5] -, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. No. 16 (1955). MR 17, 763. MR 0075539 (17:763c)
  • [6] G. H. Hardy and J. E. Littlewood, A problem concerning majorants of Fourier series, Quart. J. Math. 6 (1935), 304-315.
  • [7] S. Helgason, Multipliers of Banach algebras, Ann. of Math. (2) 64 (1956), 240-254. MR 18, 494. MR 0082075 (18:494c)
  • [8] I. Kaplansky, Dual rings, Ann. of Math. (2) 49 (1948), 689-701. MR 10, 7. MR 0025452 (10:7b)
  • [9] W. Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Appl. Math., no. 12, Interscience, New York, 1962. MR 27 #2808. MR 0152834 (27:2808)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0271640-X
Keywords: Derived algebra, $ \Lambda (p)$ sets, multiplier, unconditionally convergent Fourier series
Article copyright: © Copyright 1971 American Mathematical Society

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