Funded by The Danish National Research Foundation

MPS-RR 2004-15

June 2004

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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