Centered operators
Let be the wreath product of a compact group T with the infinite symmetric group . We study the characters of factor representations of finite type of G, and give a formula which expresses all the characters explicitly.
We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include where uₙ and are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form where and are free semicircular elements of variance α and β.