Hilbert-Schmidt differences of composition operators on the Bergman space

Boo Rim Choe, Takuya Hosokawa, Hyung Woon Koo

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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
Volume269
Issue number3-4
DOIs
Publication statusPublished - 2011 Dec 1

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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