Noncommutative Vitali-Hahn-Saks Theorem holds precisely for finite $W^\ast$-algebras
Operator Algebras
2007-11-02 v1 Functional Analysis
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.
Keywords
Cite
@article{arxiv.0711.0135,
title = {Noncommutative Vitali-Hahn-Saks Theorem holds precisely for finite $W^\ast$-algebras},
author = {E. Chetcuti and J. Hamhalter},
journal= {arXiv preprint arXiv:0711.0135},
year = {2007}
}
Comments
8 pages