Approximately transitive flows and ITPFI factors-Reference-Cited by-同舟云学术

Approximately transitive flows and ITPFI factors

Published:1985-06 Issue:2 Volume:5 Page:203-236
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

Connes A.,Woods E. J.

Abstract

AbstractWe define a new property of a Borel group action on a Lebesgue measure space, which we call approximate transitivity. Our main results are (i) a type III0 hyperfinite factor is ITPFI if and only if its flow of weights is approximately transitive, and (ii) for ergodic transformations preserving a finite measure, approximate transitivity implies zero entropy.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference23 articles.

1. Hyperfinite product factors

2. Transformations With Discrete Spectrum are Stacking Transformations

3. ITPFI factors—a survey

4. The equivalence of various definitions for a properly infinite von Neumann algebra to be approximately finite dimensional

5. The flow of weights on factors of type ${\rm III}$

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