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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: [email protected]@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: [email protected]@math.u-bordeaux1.fr
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Abstract

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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

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