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