A Linearization of Connes' Embedding Problem

Abstract

We show that Connes' embedding problem for II_1-factors is equivalent to a statement about distributions of sums of self-adjoint operators with matrix coefficients. This is an application of a linearization result for finite von Neumann algebras, which is proved using asymptotic second order freeness of Gaussian random matrices.

25pp

References in corpus (1)

• A non-commutative, analytic version of Hilbert's 17-th problem in type II${}_1$ von Neumann algebras

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• Cyclic Hilbert spaces and Connes' embedding problem