The classification problem for von Neumann factors

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We prove that it is not possible to classify separable von Neumann factors of types $\II_1$, $\II_\infty$ or $\III_λ$, $0\leq λ\leq1$, up to isomorphism by a Borel measurable assignment of "countable structures" as invariants. In particular the isomorphism relation of type $\II_1$ factors is not smooth. We also prove that the isomorphism relation for von Neumann $\II_1$ factors is analytic, but is not Borel.
To appear in the Journal of Functional Analysis

Keywords

Operator Algebras, Logic

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/224769

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0903.4484
 http://arxiv.org/abs/0903.4484

Collections

arXiv