Moment Formulas For The Quasi-Nilpotent DT-Operator

Let T be the quasi-nilpotent DT-operator. By use of Voiculescu's amalgamated R-transform we compute the moments 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...

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Bibliographic Details
Published in:arXiv.org 2004-06
Main Authors: Aagaard, L, Haagerup, U
Format: Article
Language:English
Subjects:
Operators (mathematics)
Yttrium
Online Access:Get full text
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Summary:Let T be the quasi-nilpotent DT-operator. By use of Voiculescu's amalgamated R-transform we compute the moments 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 Śniady's formula for the moments \(\tau(((T^*)^k T^k)^n)\) for \(k,n\in \mathbb N\).
ISSN:2331-8422