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Martingales on von Neumann algebras

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  • Cuculescu, I.

Abstract

We consider L1 bounded martingales on a von Neumann algebra with respect to a given ascending sequence of von Neumann subalgebras as functionals on the C*-algebra which is the uniform closure of the union of those subalgebras. We define the singular martingales, prove the "Krickeberg decomposition theorem," some convergence of the "almost sure" type theorems, and give preliminary results concerning the problem of existence of nonnull singular martingales.

Suggested Citation

  • Cuculescu, I., 1971. "Martingales on von Neumann algebras," Journal of Multivariate Analysis, Elsevier, vol. 1(1), pages 17-27, April.
    • Handle: RePEc:eee:jmvana:v:1:y:1971:i:1:p:17-27
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    Cited by:

    1. Congbian Ma & Liping Fan & Xiaoyan Zhang & Xin Li, 2023. "Duality and interpolation for symmetric Banach spaces of noncommutative quasi-martingales," Indian Journal of Pure and Applied Mathematics, Springer, vol. 54(2), pages 630-640, June.

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