Toeplitz and Hankel matrices on Cn

It is known that the characterizations of the Toeplitz operator T-psi on H-2 and also the Hankel operator H-psi on H-2 by using the simple unilateral shift T-z. Recently, some characterization of the normal Toeplitz matrix truncated on C-n is given by D.R.Farenich, M. Krupnik, N. Krupnik: and W. Y. Lee [1] and, independently, by T.Ito [2]. In this paper, we shall give some characterizations of the Toeplitz matrix and also the Hankel matrix truncated on C-n.