Martingales on von Neumann algebras

I. Cuculescu

Journal of Multivariate Analysis, 1971, vol. 1, issue 1, 17-27

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.

Keywords: faithful; normal; finite; trace; L1; bounded; martingale; uniformly; integrable; martingale; singular; martingale; bidual; of; a; C*; algebra; Krickeberg's; decomposition; a.s.; convergence; in; noncommutative; measure; theory (search for similar items in EconPapers)
Date: 1971
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Citations: View citations in EconPapers (1)

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