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Extracting almost symmetric sequences in rearrangement invariant spaces

Published online by Cambridge University Press:  24 October 2008

Yves Raynaud
Yves Raynaud
Affiliation:
Equipe d'analyse, Université Paris VI, 75252 – Paris, France
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Abstract

We extend to a wider class of rearrangement invariant spaces a result of S. Guerre concerning the extraction of almost symmetric sequences from a given weakly null sequence in Lp.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 104 , Issue 2 , September 1988 , pp. 303 - 316
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

REFERENCES

[1]Bastero, J. and Raynaud, Y.. Quotients and interpolate spaces of stable Banach spaces. Studia Math. 93 (1988), to appear.Google Scholar
[2]Bergh, J. and Lofstrom, J.. Interpolation Spaces, an Introduction (Springer-Verlag, 1976).CrossRefGoogle Scholar
[3]Berkes, I.. On Almost Symmetric Sequences in Lp. University of Texas Functional Analysis Seminar (1985–1986).Google Scholar
[4]Berkes, I. and Rosenthal, H. P.. Almost exchangeable sequences of random variables. Z. Wahrsch. Verw. Gebiete 70 (1985), 473–507.CrossRefGoogle Scholar
[5]Braverman, M. Sh.. Complementability of subspaces generated by independent functions in a symmetric space. Functional Anal. Appl. 16 (1982), 129–130.CrossRefGoogle Scholar
[6]Bretagnolle, J. and Dacunha-Castelle, D.. Applications de l'étude de certaines formes linéaires aléatoires au plongement d'espaces de Banach dans les espaces Lp. Ann. Sci. École Norm. Sup. (4) 2 (1969), 437–480.CrossRefGoogle Scholar
[7]Dacunha-Castelle, D.. Variables aléatoires échangeables et espaces d'orlicz. Séminaire Maurey-Schwartz, Ecole Polytechnique, Paris, (1974–1975).Google Scholar
[8]Feller, W.. An Introduction to Probability Theory and its Applications, vol. II (Wiley, 1966).Google Scholar
[9]Garling, D. J. H.. Stable Banach spaces, random measures and Orlicz function spaces. In Probability Measures on Groups, Lecture Notes in Math. vol. 928 (Springer-Verlag, 1982), pp. 121–175.CrossRefGoogle Scholar
[10]Gaposkhin, V. F.. Convergence and limit theorems for sequences of random variables. Theor. Probab. Appl. 17 (1972), 379–399.CrossRefGoogle Scholar
[11]Guerre, S.. Types et suites symétriques dans Lp, 1 ≤ p < + ∞. Israel J. Math. 53 (1986), 191–208CrossRefGoogle Scholar
[12]Guerre, S.. Sur les suites presque échangeables dans Lq, 1 ≤ q < 2. Israel J. Math. 56 (1986), 361–380.CrossRefGoogle Scholar
[13]Guerre, S. and Raynaud, Y.. On sequences with no almost symmetric subsequence. University of Texas Functional Analysis Seminar (1985–1986).Google Scholar
[14]Johnson, W. B., Maurey, B., Schechtman, G. and Tzafriri, L.. Symmetric structures in Banach spaces. Mem. Amer. Math. Soc. 19, no. 217 (1979).Google Scholar
[15]Krivine, J. L. and Maurey, B.. Espaces de Banach stables. Israel J. Math. 39 (1981), 273–295.CrossRefGoogle Scholar
[16]Lindenstrauss, J. and Tzafriri, L.. Classical Banach Spaces, vol. II (Springer-Verlag, 1979).CrossRefGoogle Scholar
[17]Maurey, B.. Tout sous espace de L 1 contient un lp, d'après D. Aldous. Séminaire d'analyse Fonctionnelle, Ecole Polytechnique, Paris (1979–1980).Google Scholar
[18]Raynaud, Y.. Deux nouveaux exemples d'espaces de Banach stables. C. R. Acad. Sci. Paris Sér. I Math., 292 (1981), 715–717.Google Scholar
[19]Rosenthal, H. P.. On subspaces of Lp. Ann. of Math. (2) 97 (1973), 344–373.CrossRefGoogle Scholar