MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

MPS-RR 2004-15
June 2004

# Moment Formulas for the Quasi-Nilpotent DT-Operator

by: Lars Aagaard , Uffe Haagerup

## Abstract

Let T be the quasi-nilpotent DT-operator. By use of Voiculescu's amalgamated R-transform we compute the momets of (T-\lambda 1)^*(T-\lambda 1) where \lambda\in \mathbb C, and the Brown-measure of T+\sqrt{\epsilon}Y, where Y is a circular element *-free from T for \epsilon>0. Moreover we give a new proof of \'Sniady's formula for the moments \tau(((T^*)^k T^k)^n) for k,n\in \mathbb N.

Availability: [ gzipped ps-file ] [ pdf-file ]

This paper has now been published in Internat. J. Math. 15, 581--628 (2004)