2017
Том 69
№ 9

All Issues

Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra

Chilin V. I., Muratov M. A.

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Abstract

We study the relationship between (o)-convergence and almost-everywhere convergence in the Hermite part of the ring of unbounded measurable operators associated with a finite von Neumann algebra. In particular, we prove a theorem according to which (o)-convergence and almost-everywhere convergence are equivalent if and only if the von Neumann algebra is of the type I.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 9, pp 1445-1456.

Citation Example: Chilin V. I., Muratov M. A. Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra // Ukr. Mat. Zh. - 2003. - 55, № 9. - pp. 1196-1205.

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