2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79703We use free probability techniques for computing spectra and Brown measures of some non hermitian operators in finite von Neumann algebras. Examples include u_n+u_oo where u_n and u_oo are the generators of Z_n and Z respectively, in the free product group Z_n*Z, or elliptic elements, of the form S_a+iS_b where S_a and S_b are free semi-circular elements of variance a and b. We give some pictorial evidence for connections with spectra of random matrices.LaTeX2e, 27 pages, 9 EPS figuresOperator AlgebrasSpectral Theory22D25; 46L5text