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

2012/07/14 by Leonel Robert, Robert, Leonel
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA

paper · pdf · doi:10.48550/arxiv.1207.3428

arxiv created 2012/07/14 · openalex publication_date 2012/07/14 · arxiv updated 2012/07/17 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

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.

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