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Similarity of perturbations of the shift and a different product of rational functions

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.

preprint2012arXivOpen access
Leonel Robert
math.FA
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Leonel Robert

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