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Results in Mathematics

, 74:61 | Cite as

Composition Operators on de Branges–Rovnyak Spaces

  • Emmanuel FricainEmail author
  • Muath Karaki
  • Javad Mashreghi
Article
  • 43 Downloads

Abstract

We study the compactness of the composition operator on de Branges–Rovnyak spaces. Inspired by a paper by Lyubarskii–Malinnikova on model spaces, we give some necessary and some sufficient conditions for compactness. In the paper of Lyubarskii-Malinnikova, the key point is some Bernstein inequality on model spaces due to Cohn (and based on a deep inequality of Axler–Chang–Sarason involving the Hardy–Littlewood maximal function). We generalize the result of Cohn to some subspace of a de Branges–Rovnyak space (in many cases dense) and then get a sufficient condition (analogue to Lyubarskii–Malinnikova’s condition) for compactness of the composition operator on that subspace.

Keywords

Compact operator composition operator hardy spaces de Branges–Rovnyak spaces 

Mathematics Subject Classification

Primary: 30D50 Secondary: 47B33 

Notes

Acknowledgements

We would like to thank the anonymous referee for his/her remarks especially concerning the presentation of the paper.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Emmanuel Fricain
    • 1
    Email author
  • Muath Karaki
    • 2
  • Javad Mashreghi
    • 3
  1. 1.Laboratoire Paul Painlevé, UFR de Mathématiques, Bâtiment M2Université des Sciences et Technologies Lille 1Villeneuve d’Ascq CédexFrance
  2. 2.Department of MathematicsAn–Najah National UniversityNablusPalestine
  3. 3.Départament de Mathematiques et de StatistiqueUniversité LavalQuebecCanada

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