Abstract. We are interested in computing the $\rho $-numerical radius of the truncated shift $S_n$ on $l_2^n$. This value, first computed for $\rho =2$ by Haagerup and de la Harpe, appears as a reference in constrained von Neumann inequalities. In this paper, we give an effective way of computing this value in the general case, and then some exact formulas in particular cases.

AMS Subject Classification (1991): 47A12, 15A60, 15-04; 47A63

Received November 12, 2001, and in revised form September 13, 2002. (Registered under 2897/2009.)