Characterizations of asymmetric truncated Toeplitz operators

Abstract

The aim of this paper is to investigate asymmetric truncated Toeplitz operators with $L^2$-symbols between two different model spaces given by inner functions such that one divides the other. The class of symbols corresponding to the zero operator is described. Asymmetric truncated Toeplitz operators are characterized in terms of operators of rank at most $2$, and the relations with the corresponding symbols are studied.