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On the jordan decomposition for vector measures

  • Klaus D. Schmidt
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 990)

Abstract

It is shown that a vector measure μ on an algebra of sets with values in an order complete Banach lattice G is the difference of two positive vector measures if either μ is bounded and G is an order complete AM-space with unit, or μ has bounded variation and there exists a positive contractive projection G" → G. This result is a complete counterpart to the corresponding one on the regularity of a bounded linear operator.

Keywords

Linear Operator Vector Lattice Bounded Linear Operator Bounded Variation Banach Lattice 
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References

  1. [1]
    J. Diestel and B. Faires: On vector measures. Trans. Amer. Math. Soc. 198, 253–271 (1974).MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J. Diestel and J.J. Uhl jr.: Vector Measures. Providence, Rhode Island: American Mathematical Society 1977.CrossRefzbMATHGoogle Scholar
  3. [3]
    B. Faires and T.J. Morrison: The Jordan decomposition of vector-valued measures. Proc. Amer. Math. Soc. 60, 139–143 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    H.H. Schaefer: Banach Lattices and Positive Operators. Berlin-Heidelberg-New York: Springer 1974.CrossRefzbMATHGoogle Scholar
  5. [5]
    K.D. Schmidt: A general Jordan decomposition. Arch. Math. 38 556–564 (1982).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Klaus D. Schmidt
    • 1
  1. 1.Seminar für StatistikUniversität Mannheim, A 5MannheimWest Germany

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