Turbulence and Araki-Woods factors

Details Turbulence and Araki-Woods factors Turbulence and Araki-Woods factors

2009-12-08

arxiv.org/abs/0912.1496v2

Mathematics

Operator Algebras

16 pages

Scientific paper

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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