NUMERICAL RANGES OF LARGE TOEPLITZ MATRICES

A Banach algebraic approach is proposed to study the asymptotic behavi our of the numerical ranges of certain (finite) approximation matrices of (infinite) operators. The approach works for large classes of appr oximation methods; it is examined in detail here for the finite sectio ns of Toeplitz operators and of operators which are generated by Toepl itz operators. The basic ingredient is a precise knowledge of the fini te section method for Toeplitz and related operators. (C) 1998 Elsevie r Science Inc. All rights reserved.