Positivity

, Volume 15, Issue 1, pp 49–55

Martingales in Banach lattices, II

  • Hailegebriel E. Gessesse
  • Vladimir G. Troitsky
Article

DOI: 10.1007/s11117-009-0040-5

Cite this article as:
Gessesse, H.E. & Troitsky, V.G. Positivity (2011) 15: 49. doi:10.1007/s11117-009-0040-5

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

MartingaleFiltrationBanach lattice

Mathematics Subject Classification (2000)

60G4846B42

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