Moment Formulas For The Quasi-Nilpotent DT-Operator

英文摘要：

Let T be the quasi-nilpotent DT-operator. By use of Voiculescu's amalgamated R-transform we compute the moments of $(T-λ1)^*(T-λ1)$, where $λ\in \mathbb C$, and the Brown-measure of $T+\sqrtε Y$, where Y is a circular element *-free from T for $ε>0$. Moreover we give a new proof of Śniady's formula for the moments $τ(((T^*)^k T^k)^n)$ for $k,n\in \mathbb N$.