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Moment Formulas For The Quasi-Nilpotent DT-Operator

L. Aagaard·U. Haagerup
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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 $λ\in \mathbb C$, 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 $k,n\in \mathbb N$.

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L. Aagaard, U. Haagerup. 2004-06-09. Moment Formulas For The Quasi-Nilpotent DT-Operator. https://arxiv.org/abs/math/0406170

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