Shift invariance and reflexivity of compressions of multiplication operators
M. Cristina C\^amara, Kamila Kli\'s-Garlicka, Bartosz {\L}anucha,, Marek Ptak
TL;DR
This paper investigates the shift invariance and reflexivity properties of certain operator spaces, providing new results even in symmetric cases and characterizing asymmetric dual truncated Toeplitz operators.
Contribution
It introduces new results on shift invariance and reflexivity of truncated Toeplitz operators, including a characterization of asymmetric dual operators.
Findings
Most results are new even for symmetric cases
Characterization of asymmetric dual truncated Toeplitz operators
Analysis of shift invariance and reflexivity properties
Abstract
The property of being shift invariant and being reflexive or transitive in the case of the space of (asymmetric) truncated Toeplitz operators, and the space of (asymmetric) dual truncated operators is investigated. Most of the results obtained are new even for the symmetric case. A characterization of asymmetric dual truncated Toeplitz operators is also given.
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