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

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MPS-RR 2004-15
June 2004

Moment Formulas for the Quasi-Nilpotent DT-Operator

by: Lars Aagaard , Uffe Haagerup


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.

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