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Compact differences of composition operators on weighted Dirichlet spaces

Authors
  • Allen, Robert
  • Heller, Katherine
  • Pons, Matthew
Type
Published Article
Journal
Open Mathematics
Publisher
Versita
Publication Date
Apr 03, 2014
Volume
12
Issue
7
Pages
1040–1051
Identifiers
DOI: 10.2478/s11533-013-0397-3
Source
De Gruyter
Keywords
License
Green

Abstract

Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.

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