Let X 1 and X 2 be subspaces of quotients of R ⊕ OH and C ⊕ OH respectively. We use new free probability techniques to construct a completely isomorphic embedding of the Haagerup tensor product X 1 ⊗ h X 2 into the predual of a sufficiently large QWEP von Neumann algebra. As an immediate application, given any 1 < q ≤ 2, our result produces a completely isomorphic embedding of ℓq (equipped with...

It is well known that a measured groupoid G defines a von Neumann algebra W ∗(G), and that a Lie groupoid G canonically defines both a C∗-algebra C∗(G) and a Poisson manifold A∗(G). We construct suitable categories of measured groupoids, Lie groupoids, von Neumann algebras, C∗-algebras, and Poisson manifolds, with the feature that in each case Morita equivalence comes down to isomorphism of obj...

Abstract We prove a double commutant theorem for separable subalgebras of wide class corona C * -algebras, largely resolving problem posed by Pedersen in 1988. Double theorems originated with von Neumann, whose seminal result evolved into an entire field now called Neumann algebra theory. Voiculescu later proved -algebraic the Calkin algebra. similar much more general so-called -algebras.

A pure state f of a von Neumann algebra M is called classically normal if f is normal on any von Neumann subalgebra of M on which f is multiplicative. Assuming the continuum hypothesis, a separably represented von Neumann algebra M has classically normal, singular pure states iff there is a central projection p ∈ M such that pMp is a factor of type I∞, II, or III. DEFINITION: A pure state f of ...

To a real Hilbert space and a one-parameter group of orthogonal transformations we associate a C∗-algebra which admits a free quasi-free state. This construction is a freeprobability analog of the construction of quasi-free states on the CAR and CCR algebras. We show that under certain conditions, our C∗-algebras are simple, and the free quasi-free states are unique. The corresponding von Neuma...

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees there exists a limit graphing and thus an associated Type-II1 von Neumann algebra. The Kesten-von Neumann-Serre spectral measure of the Laplacian on the limit graphing is the weak limit of the spectral measures of the Laplacians of the finite graphs. Using this limit techniques we prove a Cheeger type ...