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

• Autorzy: Philippe Biane , Franz Lehner
• Języki publikacji: EN

Abstrakty

EN

We use free probability techniques to compute spectra and Brown measures 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 $S_{α} + iS_{β}$ where $S_{α}$ and $S_{β}$ are free semicircular elements of variance α and β.

Kategorie tematyczne

• 43A05: Measures on groups and semigroups, etc.
• 46L54: Free probability and free operator algebras
• 22D25: C * -algebras and W * -algebras in relation to group representations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2001
• Tom: 90
• Numer: 2
• Strony: 181-211

Daty

wydano

2001

Twórcy

autor

Philippe Biane

• CNRS, DMA, 45 rue d'Ulm, 75005 Paris, France

autor

Franz Lehner

• Institut für Analysis und Numerik, Johannes Kepler Universität Linz, 4040 Linz, Austria
• Équipe d'Analyse, Université Paris 6, Boîte 186, Tour 46-0, 4, place Jussieu, 75252 Paris Cedex 05, France

Identyfikatory

DOI

10.4064/cm90-2-3