Compact linear combination of composition operators on Bergman spaces

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Abstract

Motivated by the question of Shapiro and Sundberg raised in 1990, study on linear combinations of composition operators has been a topic of growing interest. In this paper, we completely characterize the compactness of any finite linear combination of composition operators with general symbols on the weighted Bergman spaces in two classical terms: one is a function theoretic characterization of Julia-Carathéodory type and the other is a measure theoretic characterization of Carleson type. Our approach is completely different from what has been known so far.

Original languageEnglish
Article number108393
JournalJournal of Functional Analysis
Volume278
Issue number5
DOIs
Publication statusPublished - 2020 Mar 15

Keywords

  • Compact operator
  • Composition operator
  • Linear combination
  • Weighted Bergman space

ASJC Scopus subject areas

  • Analysis

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