Turbulence and Araki-Woods factors

TY - JOUR

T1 - Turbulence and Araki-Woods factors

AU - Sasyk, R.

AU - Törnquist, A.

AU - Törnquist, Asger Dag

PY - 2010/11/1

Y1 - 2010/11/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=77955662804&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2010.06.018

DO - 10.1016/j.jfa.2010.06.018

M3 - Journal article

AN - SCOPUS:77955662804

SN - 0022-1236

VL - 259

SP - 2238

EP - 2252

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 9

ER -