Guangfu Cao, Li He
Published 2023-04-04Version 1
It is well known that the composition operator on Hardy or Bergman space has a closed range if and only if its Navanlinna counting function induces a reverse Carleson measure. Similar conclusion is not available on the Dirichlet space. Specifically, the reverse Carleson measure is not enough to ensure that the range of the corresponding composition operator is closed. However, under certain assumptions, we in this paper set the necessary and sufficient condition for a composition operator on the Dirichlet space to have closed range.
Wandering subspaces of the Bergman space and the Dirichlet space over polydisc
Compact composition operators on the Dirichlet space and capacity of sets of contact points
A characterization of the existence of zeros for operators with Lipschitzian derivative and closed range
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