[Banach] Abstract of a paper by Vladimir G. Troitsky and Foivos Xanthos

This is an announcement for the paper "Spaces of regular abstract martingales" by Vladimir G. Troitsky and Foivos Xanthos.

Abstract: In \cite{Troitsky:05,Korostenski:08}, the authors introduced and studied the space $\mathcal M_r$ of regular martingales on a vector lattice and the space $M_r$ of bounded regular martingales on a Banach lattice. In this note, we study these two spaces from the vector lattice point of view. We show, in particular, that these spaces need not be vector lattices. However, if the underlying space is order complete then $\mathcal M_r$ is a vector lattice and $M_r$ is a Banach lattice under the regular norm.

Archive classification: math.FA

Submitted from: foivos@ualberta.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1501.01685

or

http://arXiv.org/abs/1501.01685