Uffe Haagerup , Hanne Schultz and Steen Thorbjørnsen

A new application of random matrices : Ext ( C ∗ red ( F 2 ) ) is not a group

The mathematical legacy of Uffe Haagerup

Group-type subfactors are the simplest examples of composed subfactors that were extensively studied by Haagerup and myself. Other, more general compositions were later developed by Jones and myself, and our constructions continue to be a rich source of examples of " exotic " infinite depth subfactors. I will present several results that grew out of the idea of composing subfactors. Joachim Cun...

Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra

In this paper we generalize Brown’s spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded R–diagonal operators in this class. As a particular case, we determine the Brown measure z = xy−1, where (x, y) is a circular system in the sense of Voiculescu, and we prove that for all n ...

0 A ug 2 00 3 Non - commutative Polynomials of Independent Gaussian Random Matrices . The Real and Symplectic Cases

In [HT2] Haagerup and Thorbjørnsen prove the following extension of Voiculescu’s random matrix model (cf. [V2, Theorem 2.2]): For each n ∈ N, let X 1 , . . . ,X (n) r be a system of r independent complex self-adjoint random matrices from the class SGRM(n, 1 n), and let x1, . . . , xr be a semicircular system in a C ∗-probability space. Then for any polynomial p in r non-commuting variables the ...

Invariant Subspaces for Operators in a General II1-factor

It is shown that to every operator T in a general von Neumann factor M of type II1 and to every Borel set B in the complex plane C, one can associate a maximal, closed, T -invariant subspace, K = KT (B), affiliated with M, such that the Brown measure of T |K is concentrated on B. Moreover, K is T -hyperinvariant, and the Brown measure of PK⊥T |K⊥ is concentrated on C \ B. In particular, if T ∈ ...