Resumen de Brown measures of unbounded operators affiliated with a finite von Neumann algebra

Uffe Haagerup, Hanne Schultz

• 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 Brownmeasure 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 ofVoiculescu, and we prove that for all n ? N, zn ? Lp(M, t) if and only if 0 < p < 2 n+1 .