Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra

2006/05/10 by Uffe Haagerup, Haagerup, Uffe, Hanne Schultz +1 · 2 citations
Mathematics · #46L54 #47C15 #60B99 #Advanced Operator Algebra Research #FOS: Mathematics #Operator Algebras (math.OA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0605251

openalex publication_date 2006/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we generalize Brown's spectral distribution measure to a large class of unbounded operators affiliated with a finite von Neumann algebra. Moreover, we compute the Brown measure of all unbounded R-diagonal operators in this class. As a particular case, we determine the Brown measure of z=xy^-1, where (x,y) is a circular system in the sense of Voiculescu, and we prove that for all positive integers n, zⁿ is in L^p(M) iff 0

Citations

• R-diagonal pairs - a common approach to Haar unitaries and circular elements

Cited by

• On the Brown measure of x + i y, with x,y selfadjoint and y free Poisson
• Generalized Meixner-type free gamma distributions:convolution formulas and potential correspondence

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