On the metric of the jet bundle and similarity on Dirichlet spaces

Kui Ji, Shanshan Ji, Hyun-Kyoung Kwon, Xiaoceng Liu, Jing Xu

Published 2024-01-24Version 1

In general, it is more difficult to formulate a sufficient condition for similarity than a necessary condition. We give a sufficient condition for a Cowen-Douglas operator with a positivity condition to be similar to the backward shift operator on weighted Dirichlet space. This condition involves the holomorphic jet bundle of the eigenvector bundle of the operator.