Compact Differences of Composition Operators over Polydisks

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17 Citations (Scopus)

Abstract

Moorhouse characterized compact differences of composition operators acting on a weighted Bergman space over the unit disk of the complex plane. She also found a sufficient condition for a single composition operator to be a compact perturbation of the sum of given finitely many composition operators and studied the role of second order data in determining compact differences. In this paper, based on the characterizations due to Stessin and Zhu, of boundedness and compactness of composition operators acting from a weighted Bergman space into another, we obtain the polydisk analogues of Moorhouse's results through a different approach in main steps. In addition we find a necessary coefficient relation for compact combinations which was first noticed on the disk by Kriete and Moorhouse.

Original languageEnglish
Pages (from-to)57-91
Number of pages35
JournalIntegral Equations and Operator Theory
Volume73
Issue number1
DOIs
Publication statusPublished - 2012 May

Keywords

  • Composition operator
  • Hardy space
  • compact difference
  • polydisk
  • weighted Bergman space

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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