We announce some new results regarding the classification problem for separable von Neumann algebras. Our results are obtained by applying the notion of Borel reducibility and Hjorth's theory of turbulence to the isomorphism ...

We prove that it is not possible to classify separable von Neumann factors of types II1, II∞ or IIIλ, 0 λ 1, up to isomorphism by a Borel measurable assignment of “countable structures” as invariants. In particular the ...

Let A be a von Neumann algebra and PA the manifold of projections in A. There is a natural linear connection in PA, which in the finite dimensional case coincides with the the Levi-Civita connection of the Grassmann manifold ...

La teoría de multiplicidad espectral se generaliza para las proyecciones en un algebra conmutativa de von Neumann. La bien conocida descomposición de un álgebra de tipo I de von Neumann en una suma directa de álgebras de ...

In this paper we study the metric geometry of the space Σ of positive invertible elements of a von Neumann algebra. A with a finite, normal and faithful tracial state T. The trace induces an incomplete Riemannian  metric ...

For a semi-finite von Neumann algebra A, we study the case of equality in Young´s inequality of s-numbers for a pair of τ-measurable operators a,b, and we prove that equality is only possible if |a|^p=|b|^q. We also extend ...