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arXiv · 0711.0135

Noncommutative Vitali-Hahn-Saks Theorem holds precisely for finite $W^\ast$-algebras

E. Chetcuti·J. Hamhalter
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Abstract

It is shown that the bona fide generalization of the Vitali-Hahn-Saks Theorem to von Neumann algebras is possible if, and only if, the algebra is finite. This settles the problem on the noncommutative Vitali-Hahn-Saks Theorem completely and provides new means of characterizing finite von Neumann algebras.

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E. Chetcuti, J. Hamhalter. 2007-11-01. Noncommutative Vitali-Hahn-Saks Theorem holds precisely for finite $W^\ast$-algebras. https://arxiv.org/abs/0711.0135

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