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Computation of some examples of Brown's spectral measure in free probability

Philippe BianeFranz Lehner — 2001

Colloquium Mathematicae

We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include u + 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 S α + i S β where S α and S β are free semicircular elements of variance α and β.

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