# Journal of Operator Theory

Volume 76, Issue 1, Summer 2016  pp. 133-140.

Similarity to the backward shift operator on the Dirichlet space

Authors:  Hyun-Kyoung Kwon
Author institution: Department of Mathematics, The University of Alabama, Tuscaloosa, 35487, U.S.A.

Summary:  We give a necessary condition for a Cowen--Douglas operator to be similar to the backward shift operator on the Dirichlet space. A model theorem for weighted shifts provides an eigenvector bundle structure for the operators involved and plays a fundamental role in this geometric description.

DOI: http://dx.doi.org/10.7900/jot.2015sep19.2079
Keywords:  backward shift, Cowen-Douglas operator, Dirichlet space, eigenvector bundle, reproducing kernel, similarity