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

• Autores: Uffe Haagerup, Hanne Schultz
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 100, Nº 2, 2007, págs. 209-263
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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 .