Positivity

, Volume 15, Issue 1, pp 49–55

Martingales in Banach lattices, II

Authors

  • Hailegebriel E. Gessesse
    • Department of Mathematical and Statistical SciencesUniversity of Alberta
    • Department of Mathematical and Statistical SciencesUniversity of Alberta
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

Martingale Filtration Banach lattice

Mathematics Subject Classification (2000)

60G48 46B42

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009