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The Quarterly Journal of Mathematics Advance Access published online on February 5, 2008
The Quarterly Journal of Mathematics, doi:10.1093/qmath/ham058
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© 2007. Published by Oxford University Press. All rights reserved For permissions, please email: journals.permissions@oxfordjournals.org

NON-COMMUTATIVE VITALI–HAHN–SAKS THEOREM HOLDS PRECISELY FOR FINITE W*-ALGEBRAS

E. Chetcuti{dagger}

Department of Mathematics, Junior College, University of Malta, Msida MSD.06, Malta

J. Hamhalter {ddagger}

Czech Technical University, Faculty of Electrical Engineering, Department of Mathematics, Technicka 2, 166 27 Prague 6, Czech Republic

{dagger} Corresponding author. E-mail: emanuel.chetcuti{at}um.edu.mt

Received 26 October 2007; revised 20 November 2007
  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 non-commutative Vitali–Hahn–Saks theorem completely and provides new means of characterizing finite von Neumann algebras.

{ddagger} E-mail: hamhalte{at}math.feld.cvut.cz


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