ON VON NEUMANN'S INEQUALITY FOR COMPLEX TRIANGULAR TOEPLITZ CONTRACTIONS

We prove that von Neumann's inequality holds for circulant contractions. We show that every complex polynomial f (z(1),...,z(n)) over D-n is associated to a constant d(f) such that von Neumann's inequality can hold up to d(f), for n-tuples of commuting contractions on a Hilbert space. We characterise complex polynomials over D-n in which d(f) = 2. We introduce the properties of upper (or lower) complex triangular Toeplitz matrices. We show that von Neumann's inequality holds for n-tuples of upper (or lower) complex triangular Toeplitz contractions. We construct contractive homomorphisms.