Norms of Inverses, Spectra, and Pseudospectra of Large Truncated Wiener-Hopf Operators and Toeplitz Matrices

This paper is concerned with Wiener-Hopf integral operators on Lp and with Toeplitz operators (or matrices) on lp. The symbols of the operators are assumed to be continuous matrix functions. It is well known that the invertibility of the operator itself and of its associated operator imply the invertibility of all sufficiently large truncations and the uniform boundedness of the norms of their inverses. Quantitative statements, such as results on the limit of the norms of the inverses, can be proved in the case p = 2 by means of C∗-algebra techniques. In this paper we replace C∗-algebra methods by more direct arguments to determine the limit of the norms of the inverses and thus also of the pseudospectra of large truncations in the case of general p.