A Note on Uniformly Bounded Cocycles into Finite Von Neumann Algebras

被引：0

作者：

Boutonnet, Remi ^{[1
]}

Roydor, Jean ^{[1
]}

机构：

[1] Univ Bordeaux, Inst Math Bordeaux, 351 Cours Liberat, F-33405 Talence, France

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2018年 / 61卷 / 02期

关键词：

Borel cocycle; von Neumann algebra;

D O I：

10.4153/CMB-2017-078-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：236 / 239

页数：4

共 8 条

[1]

Abramenko P, 2008, GRAD TEXTS MATH, V248, P1

[2] Cohomology of property T groupoids and applications [J].

Anantharaman-Delaroche, C .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :977-1013

[3] Nonpositively curved metric in the positive cone of a finite von Neumann algebra [J].

Andruchow, E. ;

Larotonda, G. .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2006, 74 :205-218

[4] Bounded cocycles on finite Von Neumann algebras [J].

Bates, T ;

Giordano, T .

INTERNATIONAL JOURNAL OF MATHEMATICS, 2001, 12 (06) :743-750

[5] Unitarization of uniformly bounded subgroups in finite von Neumann algebras [J].

Miglioli, Martin .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2014, 46 :1264-1266

[6]

VASILESCU FH, 1974, ACTA SCI MATH, V36, P189

[7]

ZIMMER RJ, 1977, J LOND MATH SOC, V15, P155

[8]

ZIMMER RJ, 1984, MONOGRAPHS MATH, V0081

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