Moment methods in Padé approximation: The unitary case

Given a unitary operator T in a Hilbert space H = (H, 〈·, ·〉) convergence results for two sequences of ($\text{(n ? 1)}\text{n)}$ two-point Padé approximants to the function f(z) = 〈(I ? zT)^?1u₀, u₀〉, (u₀ ∈ H, ∥ u₀∥ = 1, z regular for T) are given. An elementary proof is also given of the well-known operator version of the trigonometric moment problem, not using the solution of the classical trigonometric moment problem.