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

Philippe Biane; Franz Lehner

Colloquium Mathematicae, Tome 89 (2001), p. 181-211 / Harvested from The Polish Digital Mathematics Library

Résumé

We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include $u ₙ + u_{\infty}$ where uₙ and $u_{\infty}$ 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.

Publié le : 2001-01-01

Zbl 0988.22004

EUDML-ID : urn:eudml:doc:283888

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     title = {Computation of some examples of Brown's spectral measure in free probability},
     journal = {Colloquium Mathematicae},
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     year = {2001},
     pages = {181-211},
     zbl = {0988.22004},
     language = {en},
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Philippe Biane; Franz Lehner. Computation of some examples of Brown's spectral measure in free probability. Colloquium Mathematicae, Tome 89 (2001) pp. 181-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm90-2-3/