  Necessary and sufficient conditions are given for the similarity between two
perturbations of the (backward) shift by rank one operators, under certain
assumptions on the perturbations. The proof of similarity is based on an
explicit construction of intertwiners between the perturbations. These
intertwiners, in turn, are parametrized by the elements of a certain algebra,
with the group of "circle invertible" elements of this algebra giving rise to
invertible intertwiners.
