Abstract
AbstractMultiplication operators on the space \(L^2(\mathbb {T})\) on the unit circle \(\mathbb {T}\) with Lebesgue measure are classical operators. So are Toeplitz operators on the Hardy space \(H^2\subset L^2(\mathbb {T})\). Sarason’s paper (Oper Metrices 1:491–526, 2007) has started investigations of truncated Toeplitz operators (TTO), i.e., compressions of these multiplication operators to model spaces. If operators act between two different model spaces they are called asymmetric truncated Toeplitz operators (ATTO). Naturally the compressions of multiplication operators between orthogonal complements of model spaces can be investigated. They are called dual truncated Toeplitz operators (DTTO), or asymmetric dual truncated Toeplitz operators (ADTTO) if orthogonal complements to different model spaces are considered. In this chapter the properties of ADTTO are presented.KeywordsModel spaceMultiplication operatorDual truncated Toeplitz operatorConjugationIntertwining propertyCommutativity of operators
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