On the powers of Voiculescu's circular element
Ferenc Oravecz (2001)
Studia Mathematica
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The main result of the paper is that for a circular element c in a C*-probability space, is an R-diagonal pair in the sense of Nica and Speicher for every n = 1,2,... The coefficients of the R-series are found to be the generalized Catalan numbers of parameter n-1.