Asymmetric truncated Toeplitz operators and conjugations

Abstract

Truncated Toeplitz operators in a model space are C--symmetric with respect
to a natural conjugation in that space. We show that this and another
conjugation associated to an orthogonal decomposition possess unique
properties and we study their relations with asymmetric truncated Toeplitz
operators in terms of C--symmetry. New connections with Hankel operators are
established through this approach.