Kadison-Kastler stable factors

摘要: A conjecture of Kadison and Kastler from 1972 asks whether sufficiently close operator algebras in a natural uniform sense must be small unitary perturbations one another. For n ≥ 3 free ergodic probability measure preserving action SLn(Z) on standard nonatomic space (X,µ), write M = ((L 1 (X,µ)⋊SLn(Z))⊗R, where R is the hyperfinite II1 factor. We show that whenever represented as von Neumann algebra some Hilbert H N ⊆ B(H) toM, then there u to identity with uMu � N. This provides first nonamenable class satisfying Kastler's conjecture. also obtain stability results for crossed products L (X,µ)⋊ compar- ison map bounded usual group cohomology vanishes degree 2 module (X,µ). In this case, any such product necessarily isomorphic it. particular, result applies when group. paper complete account announced (12).