On the powers of Voiculescu's circular element
Volume 145 / 2001
Studia Mathematica 145 (2001), 85-95
MSC: 46L53, 06A07.
DOI: 10.4064/sm145-1-6
Abstract
The main result of the paper is that for a circular element $c$ in a $C^{*}$-probability space, $( c^n,c^{n^{*}}) $ is an $R$-diagonal pair in the sense of Nica and Speicher for every $n=1,2,\dots$ The coefficients of the $R$-series are found to be the generalized Catalan numbers of parameter $n-1$.
