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

Research paper by Uffe Haagerup, Hanne Schultz

Indexed on: 10 May '06Published on: 10 May '06Published in: Mathematics - Operator Algebras


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).