Linear connection between composition operators on the Hardy space

Boo Rim Choe, Koeun Choi, Hyung Woon Koo, Inyoung Park

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the space of all composition operators, acting on the Hardy space over the unit disk, in the uniform operator topology. We obtain a characterization for linear connection between composition operators. As one of applications, we see that the set of all compact composition operators is a polygonally connected component, in sharp contrast to the known fact that this set is properly contained in a path connected component. When the inducing maps have “good” boundary behavior in the sense of higher-order data and order of contact, we extend/recover the Kriete-Moorhouse characterization for linear connection through a completely different approach relying on our results. We also notice some results in conjunction with the Bergman space case. Several questions motivated by our results are included.

Original languageEnglish
Article number126402
JournalJournal of Mathematical Analysis and Applications
Volume515
Issue number1
DOIs
Publication statusPublished - 2022 Nov 1

Keywords

  • Composition operators
  • Hardy space
  • Higher-order data
  • Linearly connected
  • Order of contact
  • Polygonally connected

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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