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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141233It 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.8 pagesOperator AlgebrasFunctional Analysis46l10; 46l30Noncommutative Vitali-Hahn-Saks Theorem holds precisely for finite $W^\ast$-algebrastext