Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T07:04:53.430Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Uniformly Bounded Cocycles into Finite Von Neumann Algebras

Published online by Cambridge University Press:  20 November 2018

Remi Boutonnet  and
Jean Roydor
Remi Boutonnet
Affiliation:
Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 Cours de la Libération, 33405 Talence Cedex, France email: remi.boutonnet@gmail.comjean.roydor@math.u-bordeaux1.fr
Jean Roydor
Affiliation:
Institut de Mathématiques de Bordeaux, Université de Bordeaux, 351 Cours de la Libération, 33405 Talence Cedex, France email: remi.boutonnet@gmail.comjean.roydor@math.u-bordeaux1.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a short proof of a result of T. Bates and T. Giordano stating that any uniformly bounded Borel cocycle into a finite von Neumann algebra is cohomologous to a unitary cocycle. We also point out a separability issue in their proof. Our approach is based on the existence of a non-positive curvature metric on the positive cone of a finite von Neumann algebra.

Keywords

46L5546L4022D40Borel cocyclevon Neumann algebra
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 2 , 01 June 2018 , pp. 236 - 239
Copyright
Copyright © Canadian Mathematical Society 2018

References

[1] Abramenko, P. and Brown, K. S., Buildings. Theory and applications. Graduate Texts in Mathematics, 248, Springer, New York, 2008.Google Scholar
[2] Anantharaman-Delaroche, C., Cohomology ofproperty (T) groupoids and applications. Ergodic Theory Dynam. Systems 25(2005), 977–1013. http://dx.doi.org/10.1017/S014338570400884 Google Scholar
[3] Andruchow, E. and Larotonda, G., Nonpositively curved metric in the positive cone of a finite von Neumann algebra. J. London Math. Soc. (2) 74(2006), no. 1, 205–218. http://dx.doi.Org/10.1112/S0024610706022848 Google Scholar
[4] Bates, T. and Giordano, T., Bounded cocycles on finite von Neumann algebras. Internat. J. Math. 12(2001), no. 6, 743–750.http://dx.doi.Org/10.1142/S0129167X0100085X Google Scholar
[5] Miglioli, M., Unitarization oj uniformly bounded subgroups infinite von Neumann algebras. Bull. Lond. Math. Soc. 46(2014), 1264–1266.http://dx.doi.Org/10.1112/blms/bdu080 Google Scholar
[6] Vasilescu, E-H. and Zsidó, L., Uniformly bounded groups infinite W*-algebras. Acta Sei. Math.(Szeged) 36(1974), 189–192.Google Scholar
[7] Zimmer, R. J., Compactness conditions on cocycles of ergodic transformation groups. J. London Math. Soc. (2) 15(1977), no. 1,155–163.http://dx.doi.Org/10.1112/jlms/s2-15.1.55 Google Scholar
[8] Zimmer, R. J., Ergodic theory and semisimple groups. Monographs in Mathematics, 81, Birkhäuser Verlag, Basel, 1984.Google Scholar