Turbulence and Araki-Woods factors

R. Sasyk; A. Törnquist; Asger Dag Törnquist

doi:10.1016/j.jfa.2010.06.018

Turbulence and Araki-Woods factors

R. Sasyk, A. Törnquist, Asger Dag Törnquist

Department of Mathematical Sciences

8 Citations (Scopus)

Abstract

Using Baire category techniques we prove that Araki-Woods factors are not classifiable by countable structures. As a result, we obtain a far reaching strengthening as well as a new proof of the well-known theorem of Woods that the isomorphism problem for ITPFI factors is not smooth. We derive as a consequence that the odometer actions of Z that preserve the measure class of a finite non-atomic product measure are not classifiable up to orbit equivalence by countable structures.

Original language	English
Journal	Journal of Functional Analysis
Volume	259
Issue number	9
Pages (from-to)	2238-2252
Number of pages	15
ISSN	0022-1236
DOIs	https://doi.org/10.1016/j.jfa.2010.06.018
Publication status	Published - 1 Nov 2010

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10.1016/j.jfa.2010.06.018

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AB - Using Baire category techniques we prove that Araki-Woods factors are not classifiable by countable structures. As a result, we obtain a far reaching strengthening as well as a new proof of the well-known theorem of Woods that the isomorphism problem for ITPFI factors is not smooth. We derive as a consequence that the odometer actions of Z that preserve the measure class of a finite non-atomic product measure are not classifiable up to orbit equivalence by countable structures.

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Turbulence and Araki-Woods factors

Abstract

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