Article

Positivity

, Volume 15, Issue 1, pp 49-55

Martingales in Banach lattices, II

  • Hailegebriel E. GessesseAffiliated withDepartment of Mathematical and Statistical Sciences, University of Alberta
  • , Vladimir G. TroitskyAffiliated withDepartment of Mathematical and Statistical Sciences, University of Alberta Email author 

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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