Almost-Everywhere Convergence and (o)-Convergence in Rings of Measurable Operators Associated with a Finite von Neumann Algebra |
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Authors: | Muratov M. A. Chilin V. I. |
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Affiliation: | (1) Tavria National University, Simferopol;(2) Uzbekistan National University, Tashkent, Uzbekistan |
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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. |
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