2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59713We 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 figuresOperator Algebras22D25, 46L54; 15A52, 43A05, 60J15text