Computation of some examples of brown’s spectral measure in free probability

Abstract

We use free probability techniques to compute spectra and Brown mea- sures of some non-hermitian operators in finite von Neumann algebras. Examples include un+u∞ where un and u∞ are the generators of Zn and Z respectively, in the free product ℤn * ℤ, or elliptic elements of the form Sα + iSβ where Sα and Sβ are free semicircular elements of variance α and β.