On the computation of spectra in free probability

Details On the computation of spectra in free probability On the computation of spectra in free probability

2000-08-11

arxiv.org/abs/math/0008084v1

J. Funct. Anal. 183 (2001), no. 2, 451--471

Mathematics

Operator Algebras

LaTeX2e, 15 pages, 3 figures

Scientific paper

10.1006/jfan.2001.3748

We use free probability techniques to compute borders of spectra of non hermitian operators in finite von Neumann algebras which arise as `free sums' of `simple' operators. To this end, the resolvent is analyzed with the aid of the Haagerup inequality. Concrete examples coming from reduced C*-algebras of free product groups and leading to systems of polynomial equations illustrate the approach.

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