On the computation of spectra in free probability
arXiv:math/0008084 · doi:10.1006/jfan.2001.3748
Abstract
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.
LaTeX2e, 15 pages, 3 figures