TY - JOUR
T1 - The classification problem for von Neumann factors
AU - Sasyk, R.
AU - Törnquist, Asger Dag
PY - 2009/4/15
Y1 - 2009/4/15
N2 - We prove that it is not possible to classify separable von Neumann factors of types II, II or III, 0 ≤ λ ≤ 1, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants. In particular the isomorphism relation of type II factors is not smooth. We also prove that the isomorphism relation for von Neumann II factors is analytic, but is not Borel.
AB - We prove that it is not possible to classify separable von Neumann factors of types II, II or III, 0 ≤ λ ≤ 1, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants. In particular the isomorphism relation of type II factors is not smooth. We also prove that the isomorphism relation for von Neumann II factors is analytic, but is not Borel.
UR - http://www.scopus.com/inward/record.url?scp=62049085600&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2008.11.010
DO - 10.1016/j.jfa.2008.11.010
M3 - Journal article
AN - SCOPUS:62049085600
SN - 0022-1236
VL - 256
SP - 2710
EP - 2724
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 8
ER -