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The commutant and invariant subspaces for dual truncated Toeplitz operators. (English) Zbl 1507.47071

Summary: Dual truncated Toeplitz operators on the orthogonal complement of the model space \(K_u^2(=H^2\ominus uH^2)\) with \(u\) nonconstant inner function are defined to be the compression of multiplication operators to the orthogonal complement of \(K_u^2\) in \(L^2\). In this paper, we give a complete characterization of the commutant of dual truncated Toeplitz operator \(D_z\), and we even obtain the commutant of all dual truncated Toeplitz operators with bounded analytic symbols. Moreover, we describe the nontrival invariant subspaces of \(D_z\).

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
47A15 Invariant subspaces of linear operators
42B30 \(H^p\)-spaces
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