A remark about Λ(𝑝)-sets and Rosenthal sets

Li, Daniel

doi:10.1090/S0002-9939-98-04455-4

A remark about $\Lambda (p)$-sets and Rosenthal sets
HTML articles powered by AMS MathViewer

by Daniel Li PDF

Proc. Amer. Math. Soc. 126 (1998), 3329-3333 Request permission

Abstract:

There exist $\Lambda (p)$-sets which are not Rosenthal sets.

Résumé. Il existe des ensembles $\Lambda (p)$ qui ne sont pas des ensembles de Rosenthal.

References

Ron C. Blei, On trigonometric series associated with separable, translation invariant subspaces of $L^{\infty }(G)$, Trans. Amer. Math. Soc. 173 (1972), 491–499. MR 313715, DOI 10.1090/S0002-9947-1972-0313715-8
J. R. Blum and R. Cogburn, On ergodic sequences of measures, Proc. Amer. Math. Soc. 51 (1975), 359–365. MR 372529, DOI 10.1090/S0002-9939-1975-0372529-1
Julius Blum and Bennett Eisenberg, Generalized summing sequences and the mean ergodic theorem, Proc. Amer. Math. Soc. 42 (1974), 423–429. MR 330412, DOI 10.1090/S0002-9939-1974-0330412-0
J. R. Blum, B. Eisenberg, and L.-S. Hahn, Ergodic theory and the measure of sets in the Bohr group, Acta Sci. Math. (Szeged) 34 (1973), 17–24. MR 374336
Michael Boshernitzan, Homogeneously distributed sequences and Poincaré sequences of integers of sublacunary growth, Monatsh. Math. 96 (1983), no. 3, 173–181. MR 725629, DOI 10.1007/BF01605486
J. Bourgain, Ruzsa’s problem on sets of recurrence, Israel J. Math. 59 (1987), no. 2, 150–166. MR 920079, DOI 10.1007/BF02787258
J. Bourgain, On the maximal ergodic theorem for certain subsets of the integers, Israel J. Math. 61 (1988), no. 1, 39–72. MR 937581, DOI 10.1007/BF02776301
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
Joseph Diestel, Sequences and series in Banach spaces, Graduate Texts in Mathematics, vol. 92, Springer-Verlag, New York, 1984. MR 737004, DOI 10.1007/978-1-4612-5200-9
J. Diestel and J. J. Uhl Jr., Vector measures, Mathematical Surveys, No. 15, American Mathematical Society, Providence, R.I., 1977. With a foreword by B. J. Pettis. MR 0453964, DOI 10.1090/surv/015
Robert E. Dressler and Louis Pigno, Rosenthal sets and Riesz sets, Duke Math. J. 41 (1974), 675–677. MR 511044
Y. Katznelson, Sequences of integers dense in the Bohr group, Proc. Royal Inst. Techn. Stockholm (1973), 79-86.
Yitzhak Katznelson, Suites aléatoires d’entiers, L’analyse harmonique dans le domaine complexe (Actes Table Ronde Internat., Centre Nat. Recherche Sci., Montpellier, 1972) Lecture Notes in Math., Vol. 336, Springer, Berlin, 1973, pp. 148–152 (French). MR 0397317
L. Kuipers and H. Niederreiter, Uniform distribution of sequences, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0419394
F. Lust-Piquard, Propriétés géométriques des sous-espaces invariants par translation de $L^{1}(G)$ et $C(G)$, Séminaire sur la Géométrie des Espaces de Banach (1977–1978), École Polytech., Palaiseau, 1978, pp. Exp. No. 26, 9 (French). MR 520223
Françoise Lust-Piquard, Éléments ergodiques et totalement ergodiques dans $L^{\infty }(\Gamma )$, Studia Math. 69 (1980/81), no. 3, 191–225 (French, with English summary). MR 647138, DOI 10.4064/sm-69-3-191-225
Françoise Lust-Piquard, Bohr local properties of $C_\Lambda (T)$, Colloq. Math. 58 (1989), no. 1, 29–38. MR 1028158, DOI 10.4064/cm-58-1-29-38
Yves Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87–99 (French). MR 227697, DOI 10.4064/sm-30-1-87-99
Haskell P. Rosenthal, On trigonometric series associated with weak$^{\ast }$ closed subspaces of continuous functions, J. Math. Mech. 17 (1967), 485–490. MR 0216229, DOI 10.1512/iumj.1968.17.17029
Walter Rudin, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203–227. MR 0116177, DOI 10.1512/iumj.1960.9.59013
Ivan Singer, Bases in Banach spaces. I, Die Grundlehren der mathematischen Wissenschaften, Band 154, Springer-Verlag, New York-Berlin, 1970. MR 0298399, DOI 10.1007/978-3-642-51633-7