Non-commutative martingale VMO-spaces
Volume 191 / 2009
Studia Mathematica 191 (2009), 39-55
MSC: Primary 46B03, 46L52; Secondary 46B10.
DOI: 10.4064/sm191-1-3
Abstract
We study Banach space properties of non-commutative martingale VMO-spaces associated with general von Neumann algebras. More precisely, we obtain a version of the classical Kadets–Pełczyński dichotomy theorem for subspaces of non-commutative martingale VMO-spaces. As application we prove that if $\cal M$ is hyperfinite then the non-commutative martingale VMO-space associated with a filtration of finite-dimensional von Neumannn subalgebras of $\cal M$ has property (u).
