Composition operators with closed range on the Dirichlet space

It is well known that the composition operator on Hardy or Bergman space has a closed range if and only if its Nevanlinna 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 ensu...

Full description

Saved in:
Bibliographic Details
Published in:Banach journal of mathematical analysis 2024-04, Vol.18 (2), Article 27
Main Authors: Cao, Guangfu, He, Li
Format: Article
Language:English
Subjects:
Functional Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Original Paper
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is well known that the composition operator on Hardy or Bergman space has a closed range if and only if its Nevanlinna 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.
ISSN:2662-2033
1735-8787
DOI:10.1007/s43037-024-00334-0