Abstract
We present an operator equation characterization of a dual truncated Toeplitz (DTT) operator using the compressed shift operator. This characterization is an analogue of the classical characterization of a Toeplitz operator [2] and the more recent characterization of a truncated Toeplitz operator [32]. As applications of this characterization, we give short proofs and refinements of some basic properties of DTT operators which were obtained in [9], [10] by more complicated methods. Furthermore, we determine when a DTT operator is normal, and when two DTT operators commute. We identify the commutant of the compressed shift which is a commutant lifting theorem in spirit.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
