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

@inproceedings{Haagerup2007BrownMO,
  title={Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra},
  author={Uffe Haagerup and Hanne Schultz},
  year={2007}
}
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 z = xy−1, where (x, y) is a circular system in the sense of Voiculescu, and we prove that for all n ∈ N, zn ∈ Lp(M, τ) if and only if 0 < p < 2 n+1 . 
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