@article{5a5ee1ee9222454c982b3198d974f1b9,
title = "Kadison-Kastler stable factors",
abstract = "A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations of one another. For n ≥ 3 and a free, ergodic, probability measure-preserving action of SLn.Z on a standard nonatomic probability space (X;μ), write M =(L∞(X;μ)⋊ SLn(Z))⊗ R, where R is the hyperfinite II1-factor. We show that whenever M is represented as a von Neumann algebra on some Hilbert space H and N ⊆ B(H) is sufficiently close to M, then there is a unitary u on H close to the identity operator with uMu* = N. This provides the first nonamenable class of von Neumann algebras satisfying Kadison and Kastler's conjecture. We also obtain stability results for crossed products (L∞(X;μ)⋊ Γ whenever the comparison map from the bounded to usual group cohomology vanishes in degree 2 for the module L2(X;μ). In this case, any von Neumann algebra sufficiently close to such a crossed product is necessarily isomorphic to it. In particular, this result applies when Γ is a free group.",
author = "Jan Cameron and Erik Christensen and Sinclair, {Allan M.} and Smith, {Roger R.} and White, {Stuart A.} and Wiggins, {Alan D.}",
year = "2014",
doi = "10.1215/00127094-2819736",
language = "English",
volume = "163",
pages = "2639--2686",
journal = "Duke Mathematical Journal",
issn = "0012-7094",
publisher = "Duke University Press",
number = "14",
}