, Volume 15, Issue 1, pp 49–55 | Cite as

Martingales in Banach lattices, II

  • Hailegebriel E. Gessesse
  • Vladimir G. Troitsky


This note is a follow-up to Troitsky (Positivity 9(3):437–456, 2005). We provide several sufficient conditions for the space M of bounded martingale on a Banach lattice F to be a Banach lattice itself. We also present examples in which M is not a Banach lattice. It is shown that if F is a KB-space and the filtration is dense then F is a projection band in M.


Martingale Filtration Banach lattice 

Mathematics Subject Classification (2000)

60G48 46B42 


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  1. 1.
    Aliprantis C.D., Burkinshaw O.: Positive Operators. Academic Press Inc., Orlando (1985)MATHGoogle Scholar
  2. 2.
    Cullender S.F., Labuschagne C.C.A.: Unconditional Schauder decompositions and stopping times in the Lebesgue–Bochner spaces. J. Math. Anal. Appl. 336(2), 849–864 (2007)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Diestel, J., Uhl, J.J. Jr.: Vector Measures. Mathematical Surveys, vol. 15. American Mathematical Society, Providence (1977)Google Scholar
  4. 4.
    Meyer-Nieberg P.: Banach Lattices. Springer, Berlin (1991)MATHGoogle Scholar
  5. 5.
    Troitsky V.G.: Martingales in Banach lattices. Positivity 9(3), 437–456 (2005)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Hailegebriel E. Gessesse
    • 1
  • Vladimir G. Troitsky
    • 1
  1. 1.Department of Mathematical and Statistical SciencesUniversity of AlbertaEdmontonCanada

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