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Subspaces of LN, arithmetical diameter and sidon sets

  • J. Bourgain
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1153)

Keywords

Finite Subset Finite Union Entropy Number Banach Space Version Riesz Product 
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References

  1. [1]
    J. Bourgain: Sur les ensembles d’interpolation pour les measures discretes, C. R. Acad. Sc. Paris, t. 296, Sér I, 149–151, 1982.MathSciNetzbMATHGoogle Scholar
  2. [2]
    J. Bourgain: Propriétés de décomposition pour les ensembles de Sidon, Bulletin Soc. Math. de France, T.111, 1983, No. 4.Google Scholar
  3. [3]
    J. Bourgain: Sidon sets and Riesz products, Annales Fourier 1984, to appear.Google Scholar
  4. [4]
    J. Bourgain: Some properties of sets satisfying A(E)=B (E), Bulletin Soc. Math. de Belgique 1984, to appear.Google Scholar
  5. [5]
    J. Bourgain, V. D. Milman: Dychytomie du cotype pour les espaces invariants, C. R. Acad. Sc. Paris, to appear.Google Scholar
  6. [6]
    Bozejko, A. Pelczynski: A analogue in commutative harmonic analysis of the uniform bounded approximation property of Banach space, Sém. d’Anal. Fonct., Ecole Polytechnique, Exp 9, 1978–79.Google Scholar
  7. [7]
    S. J. Dilworth: The cotype constant and large Euclidean subspaces of normed spaces, preprint.Google Scholar
  8. [8]
    S. Drury: Sur les ensembles de Sidon, C. R. Acad. Sci. Paris, 271, 162–163 (1970).MathSciNetzbMATHGoogle Scholar
  9. [9]
    X. Fernique: Régularité des trajectoires des processus gausiens, École d’Été de St.-Flour, Springer LNM 480.Google Scholar
  10. [10]
    T. Figiel, W. B. Johnson: Large subspaces of ℓn and estimates of the Gordon-Lewis constants, Israel J. Math. 37 (1980), 92–112.MathSciNetCrossRefzbMATHGoogle Scholar
  11. [11]
    C. Graham, C. McGehee: Essays in Commutative Harmonic Analysis, Grundlehren der Math. Wissens. 238, Springer 1979.Google Scholar
  12. [12]
    C. Graham: Sur un résultat de Katznelsen et McGehee, CRASC Paris 1973.Google Scholar
  13. [13]
    J. Lopez, K. Ross: Sidon sets, New York, Marcel Dekker, 1975.zbMATHGoogle Scholar
  14. [14]
    S. Kwapien, A. Pelczynski: Absolutely summing operators and translation invariant spaces of functions on compact abelian groups, Math. Nachr. Bd. 94, 303–340 (1980).MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    L. Lindahl, F. Poulsen: Thin sets in harmonic analysis, New York, Marcel Dekker, 1971.zbMATHGoogle Scholar
  16. [16]
    M. Marcus, G. Pisier: Random Fourier series with applications to harmonic analysis, Annals of Math. Studies no 101, Princeton Univ. Press, 1981.Google Scholar
  17. [17]
    B. Maurey, G. Pisier: Séries de variables aléatoires vectorielles indpendantes et propriétis géométriques des espaces de Banach, Studia Math. 58 (1976), 45–90.MathSciNetzbMATHGoogle Scholar
  18. [18]
    V. D. Milman: Volume approach and Iteration Procedures in Local Theory of Normed Spaces, to appear in Proc. Missouri Conf. 1984, Springer LNM.Google Scholar
  19. [19]
    L. Pigno, S. Saeki: Measures whose transforms vanish at infinity, Bull. AMS 1973, 800–802.Google Scholar
  20. [20]
    G. Pisier: De nouvelles caracterisations des ensembles de Sidon, Advances in Maths, Supplementary studies, Mathematical Analysis and Applications (Part B), Vol. 7, 1981.Google Scholar
  21. [21]
    G. Pisier: Conditions d’entropie et caracterisations arithmetiques des ensembles de Sidon, preprint.Google Scholar
  22. [22]
    G. Pisier: Some applications of the complex method of interpolation to Banach lattices, Journal d’Analyse Math. de Jerusalem 35 (1979), 264–291.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    G. Pisier: Holomorphic semi-groups and the geometry of Banach spaces, Annals of Maths. 1982.Google Scholar
  24. [24]
    G. Pisier: Semi-groupes holomorphes et K-convexité, Séminaire d’Analyse Fonct., Ecole Polytechnique, Exp. 7, 1980–81.Google Scholar
  25. [25]
    G. Pisier: Remarques sur un résultat non publié de B. Maurey, Seminaire d’Analyse Fonct., Ecole Polytechnique, Exp 5, 1980–81.Google Scholar
  26. [26]
    G. Pisier: Ensembles de Sidon et espaces de cotype 2, Séminaire géometrie des espaces de Banach, Ecole Polytechnique, Exp. 14, 1977–78.Google Scholar
  27. [27]
    G. Pisier: Entimations des distances a un espace Euclidien et des constantes de projection des espaces de Banach de dimension finie, Séminaire d’Anal. Fonct., Ecole Polytechnique, Exp. 10, 1978–79.Google Scholar
  28. [28]
    M. Malliavin-Brameret, P. Malliavin: Caractérisation arithmétique des ensembles de Helson, C.R.A.Sc. Paris, Sér. A, 264 (1967), 192–193.MathSciNetzbMATHGoogle Scholar
  29. [29]
    T. Ramsay: Interpolation sets for almost periodic functions in bounded groups, preprint.Google Scholar
  30. [30]
    N. Tomczak-Jaegermann: Computing 2 summing norms with few vectors, Arkiv Mat. 17 (1979), 273–279.MathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    N. T. Varopoulos: Sous espaces de C(G) invariant par translation et de type1, Séminaire Maurey-Schwartz, Exp. 12, 1975–76.Google Scholar
  32. [32]
    N. T. Varopoulos: Tensor algebras and harmonic analysis, Acta Math., 119, 51–112(1968).MathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    J.Lindenstrauss, L. Tzafriri: Classical Banach Spaces, Springer LNM, 338 (1973).Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • J. Bourgain
    • 1
    • 2
  1. 1.Vrije Universiteit BrusselBrusselsBelgium
  2. 2.IHESBures-sur-YvetteFrance

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