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Transactions of the American Mathematical Society

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On the dichotomy problem for tensor algebras


Author: J. Bourgain
Journal: Trans. Amer. Math. Soc. 293 (1986), 793-798
MSC: Primary 43A25; Secondary 42A16, 43A46
DOI: https://doi.org/10.1090/S0002-9947-1986-0816324-7
MathSciNet review: 816324
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Abstract: Let $ I$, $ J$ be discrete spaces and $ E \subset I \times J$. Then either $ E$ is a $ V$-Sidon set (in the sense of $ [{\mathbf{2}},\S11]$), or the restriction algebra $ A(E)$ is analytic. The proof is based on probabilistic methods, involving Slépian's lemma.


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

  • [1] Jean Bourgain and Vitali Milman, Dichotomie du cotype pour les espaces invariants, C. R. Acad. Sci. Paris Sér. I Math. 300 (1985), no. 9, 263–266 (French, with English summary). MR 785065
  • [2] G. Graham and C. McGehee, Essays in commutative harmonic analysis, Springer, New York, 1982.
  • [3] X. Fernique, Regularité des trajectoires des fonctions aléatoires gaussiennes, École d’Été de Probabilités de Saint-Flour, IV-1974, Springer, Berlin, 1975, pp. 1–96. Lecture Notes in Math., Vol. 480 (French). MR 0413238
  • [4] S. Kwapień and A. Pełczyński, Absolutely summing operators and translation-invariant spaces of functions on compact abelian groups, Math. Nachr. 94 (1980), 303–340. MR 582532, https://doi.org/10.1002/mana.19800940118
  • [5] Yitzhak Katznelson and Paul Malliavin, Un critère d’analyticité pour les algĕres de restriction, C. R. Acad. Sci. Paris 261 (1965), 4964–4967 (French). MR 0203373
    Yitzhak Katznelson and Paul Malliavin, Vérification statistique de la conjecture de la dichotomie sur une classe d’algèbres de restriction, C. R. Acad. Sci. Paris Sér. A-B 262 (1966), A490–A492 (French). MR 0203374
  • [6] -, Verification statistique de la conjecture de la dichotomie sur une classe d'algèbres de restriction, C. R. Acad. Sci. Paris Sér. A--B 262 (1966), A490-A492.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1986-0816324-7
Article copyright: © Copyright 1986 American Mathematical Society