Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra
Operator Algebras
2007-05-23 v1
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).
Cite
@article{arxiv.math/0605251,
title = {Brown Measures of Unbounded Operators Affiliated with a Finite von Neumann Algebra},
author = {Uffe Haagerup and Hanne Schultz},
journal= {arXiv preprint arXiv:math/0605251},
year = {2007}
}
Comments
50 pages