Similarity of Cowen-Douglas operators to the backward Dirichlet shift

2013/07/12 by Hyun‐Kyoung Kwon, Kwon, Hyun-Kyoung
Mathematics · #47A99 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1307.3343

openalex publication_date 2013/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the same similarity characterization obtained for Cowen-Douglas operators to the backward shift operators on reproducing kernel Hilbert spaces with analytic kernels can be used to describe similarity in the Dirichlet space setting. As in previous proofs, a model theorem that allows one to get the eigenvector bundle structure of the operator plays a crucial role.

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