Symbols of compact truncated Toeplitz operators
Ryan O'Loughlin

TL;DR
This paper characterizes the dual space of a specific model space intersected with a shifted Hardy space and establishes conditions under which bounded and compact truncated Toeplitz operators have symbols of particular forms.
Contribution
It provides a duality characterization for the space $K_I^1 igcap z H^1$ and links the existence of symbols for bounded and compact truncated Toeplitz operators.
Findings
Dual space of $K_I^1 igcap z H^1$ characterized.
Bounded truncated Toeplitz operators have symbols if and only if compact ones do.
Compact operators have symbols of the form $I$ times a continuous function.
Abstract
This paper characterises the dual of the model space , where is an inner function, intersected with the shifted Hardy space, . With this duality result, it is then shown that every bounded truncated Toeplitz operator on the model space has a bounded symbol if and only if every compact truncated Toeplitz operator on has a symbol which is of the form multiplied by a continuous function.
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