Intertwining property for compressions of multiplication operators

M. Cristina Câmara, Kamila Kliś--Garlicka, Bartosz Łanucha, Marek Ptak

Published 2020-12-09, updated 2020-12-28Version 2

Following Beurling's theorem the natural compressions of the multiplication operator in the classical $L^2$ space are compressions to model spaces and to their orthogonal complements. Two possibly different model spaces are considered hence asymmetric truncated Toeplitz and asymmetric dual truncated Toeplitz operators are investigated. The main purpose of the paper is to characterize operators which intertwine compressions of the unilateral shift.