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2 Probability and Mathematical Statistics

2 2002

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Stopping and stochastic integrals as closable operators

Mohammed A. A. A.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 1

167--180

We show that for a von Neumann algebra in standard form with cyclic and separating tracial vector, and some classes of noncommutative processes on it, stopping and integrals of these processes can be treated as closable operators whose closures are affiliated to the algebra.

On the unconditional bundle convergence in L(2)-space over a von Neumann algebra

Skalski A.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 1

19--27

The Tandori theorem concerning the sufficient condition for the unconditional a.e. convergence of orthogonal series is generalized for the bundle convergencein L2-space over a σ-finite von Neumann algebra. The result implies a noncommutative version of the Orlicz theorem proved earlier by Hensz, Jajte and Paszkiewicz.