English

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