THE NUMERICAL RANGES OF A CLASS OF MATRICES

In 2000, P. Bourdon and et al conjectured that for an automorphic composition operator satisfying Tk = I for any natural number k, W(T) is not a disk. In connection to this conjecture, we introduce a class of matrices with minimal polynomial zk ¡ 1, and present some numerical and experimental results connecting to the shape of the numerical ranges of such matrices.