Decompositions of martingales of operators
by
Coenraad Labuschagne
School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Coauthors: Stuart Cullender

We extend the notion of a classical martingale in Bochner-Lebesgue spaces to that of a martingale considered as a sequence of suitable operators acting between a Banach lattice and a Banach space. A connection between convergence of such martingales and the Radon-Nikodym property in Banach spaces will be considered. We also consider analogues of the Stopping Time Theorem of Doob, the Optional Stopping Theorem and the Riesz decomposition for uniform amarts in this operator theoretic setting.

Date received: January 28, 2008