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

Uffe Haagerup·Hanne Schultz
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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, z^n is in L^p(M) iff 0<p< 2/(n+1).

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Uffe Haagerup, Hanne Schultz. 2006-05-10. Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra. https://arxiv.org/abs/math/0605251

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