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.
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Muratov, M.A., Chilin, V.I. Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra. Ukrainian Mathematical Journal 55, 1445–1456 (2003). https://doi.org/10.1023/B:UKMA.0000018006.89995.80
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DOI: https://doi.org/10.1023/B:UKMA.0000018006.89995.80