Topological structure of the set of weighted composition operators on weighted Bergman spaces of infinite order

José Bonet*, Mikael Lindström, Elke Wolf

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)

Abstract

We consider the topological space of all weighted composition operators on weighted Bergman spaces of infinite order endowed with the operator norm. We show that the set of compact weighted composition operators is path connected. Furthermore, we find conditions to ensure that two weighted composition operators are in the same path connected component if the difference of them is compact. Moreover, we compare the topologies induced by L(H) and L(Hν) on the space of bounded composition operators and give a sufficient condition for a composition operator to be isolated.

Original languageEnglish
Pages (from-to)195-210
Number of pages16
JournalIntegral Equations and Operator Theory
Volume65
Issue number2
DOIs
Publication statusPublished - Oct 2009
MoE publication typeA1 Journal article-refereed

Keywords

  • Topological structure
  • Weighted Bergman space of infinite order
  • Weighted composition operator

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