The commutant and invariant subspaces for dual truncated Toeplitz operators

Abstract

Dual truncated Toeplitz operators on the orthogonal complement of the model space K 2 u (= H 2 ⊖ uH 2 ) with u nonconstant inner function are defined to be the compression of multiplication operators to the orthogonal complement of K 2 u 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 .

Intertwining property for compressions of multiplication operators

“…Our results from Sections 4 and 5 were obtained as new even in the symmetric case θ = α. However, this special case was considered in the very recent papers [14,18].…”