Non-commutative martingale VMO-spaces

Tom 191 / 2009

Narcisse Randrianantoanina Studia Mathematica 191 (2009), 39-55 MSC: Primary 46B03, 46L52; Secondary 46B10. DOI: 10.4064/sm191-1-3

Streszczenie

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).

Autorzy

  • Narcisse RandrianantoaninaDepartment of Mathematics
    Miami University
    Oxford, OH 45056, U.S.A.
    e-mail

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