Brown measures of unbounded operators affiliated with a finite von Neumann algebra - Haagerup, Uffe; Schultz, Hanne (Mathematica Scandinavica, 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 nN, z^nL^p if and only if 0<p<2n+1.