Hilbert-Schmidt differences of composition operators on the Bergman space

Boo Rim Choe, Takuya Hosokawa, Hyungwoon Koo

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


In the setting of the weighted Bergman space over the unit disk, we characterize Hilbert-Schmidt differences of two composition operators in terms of integrability condition involving pseudohyperbolic distance between the inducing functions. We also show that a linear combination of two composition operators can be Hilbert-Schmidt, except for trivial cases, only when it is essentially a difference. We apply our results to study the topological structure of the space of all composition operators under the Hilbert-Schmidt norm topology. We first characterize components and then provide some sufficient conditions for isolation or for non-isolation.

Original languageEnglish
Pages (from-to)751-775
Number of pages25
JournalMathematische Zeitschrift
Issue number3-4
Publication statusPublished - 2011 Dec

Bibliographical note

Funding Information:
This research was supported by the Korea Research Foundation Grant funded by the Korean Government (KRF-2008-314-C00012).


  • Bergman space
  • Composition operator
  • Hilbert-Schmidt norm topology
  • Hilbert-Schmidt operator
  • Unit disk

ASJC Scopus subject areas

  • General Mathematics


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