Cancellation properties of composition operators on Bergman spaces

Hyung Woon Koo, Maofa Wang

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The compact difference of two composition operators on the Bergman spaces over the unit disc is characterized in [11] in terms of certain cancellation property of the inducing maps at every "bad" boundary points, which make each single composition operator not to be compact. In this paper, we completely characterize the compactness of a linear combination of three composition operators on the Bergman space. As one consequence of this characterization, we show that there is no cancellation property for the compactness of double difference of composition operators. More precisely, we show that if ϕ<inf>i</inf> are distinct and none of Cϕi is compact, then (C<inf>ϕ1-Cϕ2</inf>)-(C<inf>ϕ3-Cϕ1</inf>) is compact if and only if both (C<inf>ϕ1-Cϕ2</inf>) and (C<inf>ϕ3-Cϕ1</inf>) are compact.

Original languageEnglish
Pages (from-to)1174-1182
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume432
Issue number2
DOIs
Publication statusPublished - 2015 Dec 15

Keywords

  • Compactness
  • Difference of composition operators
  • Linear combination

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Cancellation properties of composition operators on Bergman spaces'. Together they form a unique fingerprint.

  • Cite this