Characterizations of asymmetric truncated Toeplitz operators
  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. Characterizations of these operators are given in terms of rank two operators. A description of the class of symbols for which the corresponding asymmetric truncated Toeplitz operator is equal to the zero operator is also given. 
Cristina C\^amara, Joanna Jurasik, Kamila Kli\'s--Garlicka, Marek Ptak
math.FA