Toeplitz Operators

Abstract

We now leave Hilbert space and turn to operators on Banach spaces. Natural generalizations of the Hilbert spaces L ² (R ₊ ) and are the weighted Lebesgue spaces L ^P(R ₊ w) and the weighted Hardy spaces H ^P(R w) respectively. Accordingly the theory of Wiener-Hopf operators we have studied in Chapters 2 and 10 bifurcates into the theory of Wiener-Hopf operators on L ^P(R ₊ w) and the theory of Toeplitz operators on H ^P(R, w). Although the final results of these two theories almost coincide, the theories are not equivalent and are based on different techniques. In the following, we first consider Toeplitz operators and turn to the (slightly more difficult) theory of Wiener-Hopf operators in the forthcoming chapters