On Hilbert sets and -spaces with no subspace isomorphic to
Colloquium Mathematicae (1995)
- Volume: 68, Issue: 1, page 67-77
- ISSN: 0010-1354
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topLi, Daniel. "On Hilbert sets and $C_{λ}(g)$-spaces with no subspace isomorphic to $c_0$." Colloquium Mathematicae 68.1 (1995): 67-77. <http://eudml.org/doc/210295>.
@article{Li1995,
author = {Li, Daniel},
journal = {Colloquium Mathematicae},
keywords = {locally compact abelian groups; Hilbert sets; Bourgain-Mikheev classes; thin subsets},
language = {eng},
number = {1},
pages = {67-77},
title = {On Hilbert sets and $C_\{λ\}(g)$-spaces with no subspace isomorphic to $c_0$},
url = {http://eudml.org/doc/210295},
volume = {68},
year = {1995},
}
TY - JOUR
AU - Li, Daniel
TI - On Hilbert sets and $C_{λ}(g)$-spaces with no subspace isomorphic to $c_0$
JO - Colloquium Mathematicae
PY - 1995
VL - 68
IS - 1
SP - 67
EP - 77
LA - eng
KW - locally compact abelian groups; Hilbert sets; Bourgain-Mikheev classes; thin subsets
UR - http://eudml.org/doc/210295
ER -
References
top- [1] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 57 (1958), 151-164. Zbl0084.09805
- [2] J. Bourgain, Sous-espaces invariants par translation sur le groupe de Cantor, C. R. Acad. Sci. Paris Sér. A 292 (1980), 39-40. Zbl0442.43016
- [3] J. Bourgain, Translation invariant complemented subspaces of , Studia Math. 75 (1982), 95-101. Zbl0495.43001
- [4] J. Bourgain, New Classes of -Spaces, Lecture Notes in Math. 889, Springer, 1983.
- [5] J. Bourgain, Propriétés de décomposition pour les ensembles de Sidon, Bull. Soc. Math. France 111 (1983), 421-428. Zbl0546.43006
- [6] J. Bourgain, Sidon sets and Riesz products, Ann. Inst. Fourier (Grenoble) 35 (1) (1985), 136-148. Zbl0578.43008
- [7] M. Déchamps-Gondim, Ensembles de Sidon topologiques, ibid. 22 (1972), 51-79.
- [9] M. Déchamps-Gondim, Sur les compacts associés aux ensembles lacunaires, les ensembles de Sidon et quelques problèmes ouverts, Publ. Math. Orsay 84-01 (1984). Zbl0537.43018
- [10] H. G. Diamond, Elementary methods in the study of the distribution of prime numbers, Bull. Amer. Math. Soc. 7 (1982), 553-589. Zbl0505.10021
- [11] J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Math. 92, Springer, 1984.
- [12] J. Diestel and J. J. Uhl Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.
- [13] R. E. Dressler and L. Pigno, Rosenthal sets and Riesz sets, Duke Math. J. 41 (1974), 675-677. Zbl0306.43006
- [14] R. E. Dressler and L. Pigno, Une remarque sur les ensembles de Rosenthal et Riesz, C. R. Acad. Sci. Paris Sér. A 280 (1975), 1281-1282. Zbl0299.43001
- [15] J. J. F. Fournier and L. Pigno, Analytic and arithmetic properties of thin sets, Pacific J. Math. 105 (1983), 115-141. Zbl0491.43006
- [16] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, M. B. Porter Lectures, Princeton Univ. Press, Princeton, N.J., 1981.
- [17] G. Godefroy, Sous-espaces bien disposés de ; applications, Trans. Amer. Math. Soc. 286 (1984), 227-249. Zbl0521.46012
- [18] G. Godefroy, On Riesz subsets of abelian discrete groups, Israel J. Math. 61 (1988), 301-331. Zbl0661.43003
- [19] G. Godefroy and B. Iochum, Arens-regularity of Banach algebras and the geometry of Banach spaces, J. Funct. Anal. 80 (1988), 47-59. Zbl0675.46017
- [20] G. Godefroy and F. Lust-Piquard, Some applications of geometry of Banach spaces to harmonic analysis, Colloq. Math. 60-61 (1990), 443-456. Zbl0759.46019
- [21] G. Godefroy et P. Saab, Quelques espaces de Banach ayant les propriétés (V) ou (V*) de A. Pełczyński, C. R. Acad. Sci. Paris Sér. I 303 (1986), 503-506. Zbl0602.46014
- [22] F. Gramain et Y. Meyer, Quelques fonctions moyenne-périodiques bornées, Colloq. Math. 33 (1975), 133-137. Zbl0334.42025
- [23] N. Hindman, Ultrafilters and combinatorial number theory, in: Lecture Notes in Math. 751, Springer, 1979, 119-184.
- [24] N. Hindman, On density, translates and pairwise sums of integers, J. Combin. Theory Ser. A 33 (1982), 147-157. Zbl0496.10036
- [25] B. Host, J.-F. Méla et F. Parreau, Analyse harmonique des mesures, Astérisque 133-134 (1986). Zbl0589.43001
- [26] D. Li, Espaces L-facteurs de leurs biduaux : bonne disposition, meilleure approximation et propriété de Radon-Nikodym, Quart. J. Math. Oxford (2) 38 (1987), 229-243. Zbl0631.46020
- [27] D. Li, Lifting properties for some quotients of -spaces and other spaces L-summand in their bidual, Math. Z. 199 (1988), 321-329. Zbl0631.46021
- [28] D. Li, A class of Riesz sets, Proc. Amer. Math. Soc. 119 (1993), 889-892. Zbl0796.43004
- [29] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, 1977. Zbl0362.46013
- [30] J. M. Lopez and K. A. Ross, Sidon Sets, Lecture Notes in Pure and Appl. Math. 13, Marcel Dekker, New York, 1975.
- [31] F. Lust-Piquard, Ensembles de Rosenthal et ensembles de Riesz, C. R. Acad. Sci. Paris Sér. A 282 (1976), 833-835. Zbl0324.43007
- [32] F. Lust-Piquard, Propriétés harmoniques et géométriques des sous-espaces invariants par translation de , thèse, Orsay, 1978. Zbl0462.43006
- [33] F. Lust-Piquard, Propriétés géométriques des sous-espaces invariants par translation de et C(G), Sém. Géom. Espaces Banach, exp. no. 26 (1977-78), Ecole Polytechnique. Zbl0462.43006
- [34] F. Lust-Piquard, L'espace des fonctions presque-périodiques dont le spectre est contenu dans un ensemble compact dénombrable a la propriété de Schur, Colloq. Math. 41 (1979), 274-284. Zbl0462.43007
- [35] F. Lust-Piquard, Eléments ergodiques et totalement ergodiques dans , Studia Math. 69 (1981), 191-225. Zbl0476.43001
- [36] F. Lust-Piquard, Bohr local properties of , Colloq. Math. 58 (1989), 29-38. Zbl0694.43005
- [37] F. Lust-Piquard and W. Schachermayer, Functions in and associated convolution operators, Studia Math. 93 (1989), 109-136. Zbl0722.43004
- [38] J.-F. Méla, Approximation diophantienne et ensembles lacunaires, Bull. Soc. Math. France Mém. 19 (1969), 26-54. Zbl0198.09404
- [39] Y. Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87-99. Zbl0159.42501
- [40] Y. Meyer, Recent advances in spectral synthesis, in: Lecture Notes in Math. 266, Springer, 1972, 239-253.
- [41] I. M. Miheev [I. M. Mikheev], On lacunary series, Math. USSR-Sb. 27 (1975), 481-502. Zbl0371.42006
- [42] I. M. Miheev [I. M. Mikheev], Trigonometric series with gaps, Analysis Math. 9 (1983), 43-55. Zbl0544.10062
- [43] M. B. Nathanson, Sumsets contained in infinite sets of integers, J. Combin. Theory Ser. A 28 (1980), 150-155. Zbl0451.10036
- [44] E. Odell and H. P. Rosenthal, A double-dual characterization of separable Banach spaces containing , Israel J. Math. 20 (1975), 375-384. Zbl0312.46031
- [45] A. Pełczyński, Banach spaces on which every unconditionally converging operator is weakly compact, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 10 (1962), 641-648. Zbl0107.32504
- [46] H. Pfitzner, L-summands in their biduals have pełczyński's property (V*), Studia Math. 104 (1993), 91-98. Zbl0815.46020
- [47] H. P. Rosenthal, On trigonometric series associated with weak* closed subspaces of continuous functions, J. Math. Mech. 17 (1967), 485-490. Zbl0194.16703
- [48] M. Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 307 (1984).
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