Numerical ranges of large Toeplitz matrices Original Research Article

A Bananch algebraic approach is proposed to study the asymptotic behaviour of the numerical ranges of certain (finite) approximation matrices of (infinite) operators. The approach works for large classes of approximation methods; it is examined in detail here for the finite sections of Toeplitz operators and of operators which are generated by Toeplitz operators. The basic ingredient is a precise knowledge of the finite section method for Toeplitz and related operators.