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Banach spaces related to α-stable measures

  • Nguyen Zui Tien
  • Aleksander Weron
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 828)

Abstract

A class Vα of Banach spaces is defined by the inequality (2) for α-stable measures, where 1≤α≤2. It is shown that if α<2 then there exists a Banach space of α-stable type which does not belong to Vα. A characterization of α-stable Radon measure in α-stable spaces from the Vα class is given for 1<α<2.

Keywords

Banach Space Radon Measure Cylinder Measure Cylindrical Measure Usual Operator Norm 
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References

  1. 1.
    A. Badrikian, S. Chevet, Measures cylindriques. Espaces de Wiener et fonctions aléatoires Gaussiens. Lecture Notes in Math. 397 (1974), Springer-Verlag.Google Scholar
  2. 2.
    S. A. Chobanjan, V. I. Tarieladze, Gaussian characterizations of certain Banach spaces, J. Mult. Anal. 7 (1977), 183–203.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    S. A. Chobanjan, A. Weron, The existence of the linear prediction for Banach space valued Gaussian process, J. Mult. Anal. (to appear).Google Scholar
  4. 4.
    Dang Hung Thang, Nguyen Zui Tien, On stable measures in Banach spaces, preprint.Google Scholar
  5. 5.
    W. Feller, An introduction to probability theory and its applications, Vol. II, 1966, John Wiley and Sons, New York.zbMATHGoogle Scholar
  6. 6.
    J. Lindenstrauss, A. Pełczynski, Absolutely summing operators in L p-spaces and their applications, Studia Math. 29 (1968), 275–326.MathSciNetzbMATHGoogle Scholar
  7. 7.
    D. Mouchtari, La topologie du type Sazonov pour les Banach et les supports Hilbertiens. Annales L’Universite de Clermont, 61 (1976), 77–87.MathSciNetzbMATHGoogle Scholar
  8. 8.
    A. Tortrat, Lois indefiniment divisibles dans un groupe topologique abelien metrisable X. Ces des espaces vectoriels, C.R. Adad. Sci. Paris, 261(1965), 4973–4975.MathSciNetzbMATHGoogle Scholar
  9. 9.
    N. N. Vakhania, Probability distributions in linear spaces, Tbilisi, 1971 (in Russian).Google Scholar
  10. 10.
    W. A. Woyczynski, Geometry and martingales in Banach spaces, Part II, in Advances in Probability and Related Topics, Vol. 4, Ed. J. Kuelbs, Marcel Dekker, Inc., New York, 1978, 267–517.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Nguyen Zui Tien
    • 1
  • Aleksander Weron
    • 1
  1. 1.Institute of MathematicsWroclaw Technical UniversityWroclawPoland

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