Positivity

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

Martingales in Banach lattices, II

  • Hailegebriel E. Gessesse
  • Vladimir G. Troitsky
Article

Abstract

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.

Keywords

Martingale Filtration Banach lattice 

Mathematics Subject Classification (2000)

60G48 46B42 

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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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