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On the Computation of Spectra in Free Probability

โœ Scribed by Franz Lehner

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
204 KB
Volume
183
Category
Article
ISSN
0022-1236

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โœฆ Synopsis

We use free probability techniques to compute borders of spectra of nonhermitian operators in finite von Neumann algebras which arise as free sums'' of simple'' operators. To this end, the resolvent is analyzed with the aid of the Haagerup inequality. Concrete examples coming from reduced C*-algebras of free product groups and leading to systems of polynomial equations illustrate the approach.

๐Ÿ“œ SIMILAR VOLUMES

R-Cyclic Families of Matrices in Free Pr
R-Cyclic Families of Matrices in Free Probability
โœ Alexandru Nica; Dimitri Shlyakhtenko; Roland Speicher ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 293 KB

We introduce the concept of ''R-cyclic family'' of matrices with entries in a noncommutative probability space; the definition consists in asking that only the ''cyclic'' noncrossing cumulants of the entries of the matrices are allowed to be nonzero. Let A 1 , ..., A s be an R-cyclic family of d ร— d