The classification problem for von Neumann factors

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Standard

The classification problem for von Neumann factors. / Sasyk, R.; Törnquist, Asger Dag.

In: Journal of Functional Analysis, Vol. 256, No. 8, 15.04.2009, p. 2710-2724.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Sasyk, R & Törnquist, AD 2009, 'The classification problem for von Neumann factors', Journal of Functional Analysis, vol. 256, no. 8, pp. 2710-2724. https://doi.org/10.1016/j.jfa.2008.11.010

APA

Sasyk, R., & Törnquist, A. D. (2009). The classification problem for von Neumann factors. Journal of Functional Analysis, 256(8), 2710-2724. https://doi.org/10.1016/j.jfa.2008.11.010

Vancouver

Sasyk R, Törnquist AD. The classification problem for von Neumann factors. Journal of Functional Analysis. 2009 Apr 15;256(8):2710-2724. https://doi.org/10.1016/j.jfa.2008.11.010

Author

Sasyk, R. ; Törnquist, Asger Dag. / The classification problem for von Neumann factors. In: Journal of Functional Analysis. 2009 ; Vol. 256, No. 8. pp. 2710-2724.

Bibtex

@article{4a547cc4c2f14c25bf1091b5df654f38,
title = "The classification problem for von Neumann factors",
abstract = "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.",
author = "R. Sasyk and T{\"o}rnquist, {Asger Dag}",
year = "2009",
month = apr,
day = "15",
doi = "10.1016/j.jfa.2008.11.010",
language = "English",
volume = "256",
pages = "2710--2724",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "8",

}

RIS

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

VL - 256

SP - 2710

EP - 2724

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 8

ER -

ID: 61337579