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Ukrainian Mathematical Journal

, Volume 55, Issue 9, pp 1445–1456 | Cite as

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

  • M. A. Muratov
  • V. I. Chilin
Article

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.

Keywords

Operator Associate Hermite Part 
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Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • M. A. Muratov
    • 1
  • V. I. Chilin
    • 2
  1. 1.Tavria National UniversitySimferopol
  2. 2.Uzbekistan National UniversityTashkentUzbekistan

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