Symbols of compact truncated Toeplitz operators

Abstract

This paper characterises the dual of the model space K 1 I , where I is an inner function, intersected with the shifted Hardy space, zH 1 . With this duality result, it is then shown that every bounded truncated Toeplitz operator on the model space K 2 I has a bounded symbol if and only if every compact truncated Toeplitz operator on K 2 I has a symbol which is of the form I multiplied by a continuous function.