On Hilbert sets and Cλ(g)-spaces with no subspace isomorphic to c0
Li, Daniel
Colloquium Mathematicae, Tome 68 (1995), p. 67-77 / Harvested from The Polish Digital Mathematics Library
Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:210295
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     author = {Li, Daniel},
     title = {On Hilbert sets and $C\_{$\lambda$}(g)$-spaces with no subspace isomorphic to $c\_0$
            },
     journal = {Colloquium Mathematicae},
     volume = {68},
     year = {1995},
     pages = {67-77},
     zbl = {0848.43006},
     language = {en},
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Li, Daniel. On Hilbert sets and $C_{λ}(g)$-spaces with no subspace isomorphic to $c_0$
            . Colloquium Mathematicae, Tome 68 (1995) pp. 67-77. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p67bwm/

[000] [1] C. Bessaga and A. Pełczyński, On bases and unconditional convergence of series in Banach spaces, Studia Math. 57 (1958), 151-164. | Zbl 0084.09805

[001] [2] J. Bourgain, Sous-espaces Lp invariants par translation sur le groupe de Cantor, C. R. Acad. Sci. Paris Sér. A 292 (1980), 39-40. | Zbl 0442.43016

[002] [3] J. Bourgain, Translation invariant complemented subspaces of Lp, Studia Math. 75 (1982), 95-101. | Zbl 0495.43001

[003] [4] J. Bourgain, New Classes of Lp-Spaces, Lecture Notes in Math. 889, Springer, 1983.

[004] [5] J. Bourgain, Propriétés de décomposition pour les ensembles de Sidon, Bull. Soc. Math. France 111 (1983), 421-428. | Zbl 0546.43006

[005] [6] J. Bourgain, Sidon sets and Riesz products, Ann. Inst. Fourier (Grenoble) 35 (1) (1985), 136-148. | Zbl 0578.43008

[006] [7] M. Déchamps-Gondim, Ensembles de Sidon topologiques, ibid. 22 (1972), 51-79.

[007]

[008] [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). | Zbl 0537.43018

[009] [10] H. G. Diamond, Elementary methods in the study of the distribution of prime numbers, Bull. Amer. Math. Soc. 7 (1982), 553-589. | Zbl 0505.10021

[010] [11] J. Diestel, Sequences and Series in Banach Spaces, Graduate Texts in Math. 92, Springer, 1984.

[011] [12] J. Diestel and J. J. Uhl Jr., Vector Measures, Math. Surveys 15, Amer. Math. Soc., 1977.

[012] [13] R. E. Dressler and L. Pigno, Rosenthal sets and Riesz sets, Duke Math. J. 41 (1974), 675-677. | Zbl 0306.43006

[013] [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. | Zbl 0299.43001

[014] [15] J. J. F. Fournier and L. Pigno, Analytic and arithmetic properties of thin sets, Pacific J. Math. 105 (1983), 115-141. | Zbl 0491.43006

[015] [16] H. Furstenberg, Recurrence in Ergodic Theory and Combinatorial Number Theory, M. B. Porter Lectures, Princeton Univ. Press, Princeton, N.J., 1981.

[016] [17] G. Godefroy, Sous-espaces bien disposés de L1; applications, Trans. Amer. Math. Soc. 286 (1984), 227-249. | Zbl 0521.46012

[017] [18] G. Godefroy, On Riesz subsets of abelian discrete groups, Israel J. Math. 61 (1988), 301-331. | Zbl 0661.43003

[018] [19] G. Godefroy and B. Iochum, Arens-regularity of Banach algebras and the geometry of Banach spaces, J. Funct. Anal. 80 (1988), 47-59. | Zbl 0675.46017

[019] [20] G. Godefroy and F. Lust-Piquard, Some applications of geometry of Banach spaces to harmonic analysis, Colloq. Math. 60-61 (1990), 443-456. | Zbl 0759.46019

[020] [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. | Zbl 0602.46014

[021] [22] F. Gramain et Y. Meyer, Quelques fonctions moyenne-périodiques bornées, Colloq. Math. 33 (1975), 133-137. | Zbl 0334.42025

[022] [23] N. Hindman, Ultrafilters and combinatorial number theory, in: Lecture Notes in Math. 751, Springer, 1979, 119-184.

[023] [24] N. Hindman, On density, translates and pairwise sums of integers, J. Combin. Theory Ser. A 33 (1982), 147-157. | Zbl 0496.10036

[024] [25] B. Host, J.-F. Méla et F. Parreau, Analyse harmonique des mesures, Astérisque 133-134 (1986). | Zbl 0589.43001

[025] [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. | Zbl 0631.46020

[026] [27] D. Li, Lifting properties for some quotients of L1-spaces and other spaces L-summand in their bidual, Math. Z. 199 (1988), 321-329. | Zbl 0631.46021

[027] [28] D. Li, A class of Riesz sets, Proc. Amer. Math. Soc. 119 (1993), 889-892. | Zbl 0796.43004

[028] [29] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I, Ergeb. Math. Grenzgeb. 92, Springer, 1977. | Zbl 0362.46013

[029] [30] J. M. Lopez and K. A. Ross, Sidon Sets, Lecture Notes in Pure and Appl. Math. 13, Marcel Dekker, New York, 1975.

[030] [31] F. Lust-Piquard, Ensembles de Rosenthal et ensembles de Riesz, C. R. Acad. Sci. Paris Sér. A 282 (1976), 833-835. | Zbl 0324.43007

[031] [32] F. Lust-Piquard, Propriétés harmoniques et géométriques des sous-espaces invariants par translation de L(G), thèse, Orsay, 1978. | Zbl 0462.43006

[032] [33] F. Lust-Piquard, Propriétés géométriques des sous-espaces invariants par translation de L1(G) et C(G), Sém. Géom. Espaces Banach, exp. no. 26 (1977-78), Ecole Polytechnique. | Zbl 0462.43006

[033] [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. | Zbl 0462.43007

[034] [35] F. Lust-Piquard, Eléments ergodiques et totalement ergodiques dans L(Γ), Studia Math. 69 (1981), 191-225. | Zbl 0476.43001

[035] [36] F. Lust-Piquard, Bohr local properties of CΛ(T), Colloq. Math. 58 (1989), 29-38. | Zbl 0694.43005

[036] [37] F. Lust-Piquard and W. Schachermayer, Functions in L(G) and associated convolution operators, Studia Math. 93 (1989), 109-136. | Zbl 0722.43004

[037] [38] J.-F. Méla, Approximation diophantienne et ensembles lacunaires, Bull. Soc. Math. France Mém. 19 (1969), 26-54. | Zbl 0198.09404

[038] [39] Y. Meyer, Spectres des mesures et mesures absolument continues, Studia Math. 30 (1968), 87-99. | Zbl 0159.42501

[039] [40] Y. Meyer, Recent advances in spectral synthesis, in: Lecture Notes in Math. 266, Springer, 1972, 239-253.

[040] [41] I. M. Miheev [I. M. Mikheev], On lacunary series, Math. USSR-Sb. 27 (1975), 481-502. | Zbl 0371.42006

[041] [42] I. M. Miheev [I. M. Mikheev], Trigonometric series with gaps, Analysis Math. 9 (1983), 43-55. | Zbl 0544.10062

[042] [43] M. B. Nathanson, Sumsets contained in infinite sets of integers, J. Combin. Theory Ser. A 28 (1980), 150-155. | Zbl 0451.10036

[043] [44] E. Odell and H. P. Rosenthal, A double-dual characterization of separable Banach spaces containing l1, Israel J. Math. 20 (1975), 375-384. | Zbl 0312.46031

[044] [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. | Zbl 0107.32504

[045] [46] H. Pfitzner, L-summands in their biduals have pełczyński's property (V*), Studia Math. 104 (1993), 91-98. | Zbl 0815.46020

[046] [47] H. P. Rosenthal, On trigonometric series associated with weak* closed subspaces of continuous functions, J. Math. Mech. 17 (1967), 485-490. | Zbl 0194.16703

[047] [48] M. Talagrand, Pettis integral and measure theory, Mem. Amer. Math. Soc. 307 (1984).