MOMENT FORMULAS FOR THE QUASI-NILPOTENT DT-OPERATOR

Abstract

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 [Formula: see text], and the Brown-measure of [Formula: see text], where Y is a circular element *-free from T for ∊>0. Moreover we give a new proof of Śniady's formula for the moments τ(((T*)kTk)n) for k,n∈ℕ.