Turbulence and Araki–Woods factors

Published Date
Journal of Functional Analysis
1 November 2010, Vol.259(9):2238–2252, doi:10.1016/j.jfa.2010.06.018
Open Archive, Elsevier user license

• Author 

• Román Sasyk ^a,,
• Asger Törnquist ^b,

• aInstituto Argentino de Matemáticas – CONICET, Saavedra 15, Piso 3 (1083), Buenos Aires, Argentina
• bKurt Gödel Research Center, University of Vienna, Währinger Strasse 25, 1090 Vienna, Austria

Received 8 February 2010. Accepted 23 June 2010. Available online 17 July 2010. Communicated by S. Vaes

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   that preserve the measure class of a finite non-atomic product measure are not classifiable up to orbit equivalence by countable structures.

Keywords

Von Neumann algebras

Classification of factors

Descriptive set theory

Borel reducibility

Turbulence

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