Similarity of Operators in the Bergman Space Setting
  We give a necessary and sufficient condition for an n-hypercontraction to be similar to the backward shift operator in a weighted Bergman space. This characterization serves as a generalization of the description given in the Hardy space setting, where the geometry of the eigenvector bundles of the operators is used. 
Ronald G. Douglas, Hyun-Kyoung Kwon, and Sergei Treil
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