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Composition Operators on Function Spaces on the Halfplane: Spectra and Semigroups

In: Multivariable Operator Theory

Author

Listed:
  • I. Chalendar

    (Université Gustave Eiffe, LAMA, (UMR 8050), UPEM, UPEC, CNRS)

  • J. R. Partington

    (University of Leeds, School of Mathematics)

Abstract

This paper considers composition operators on Zen spaces (a class of weighted Bergman spaces of the right half-plane related to weighted function spaces on the positive half-line by means of the Laplace transform). Generalizations are given to work of Kucik on norms and essential norms, to work of Schroderus on (essential) spectra, and to work by Arvanitidis and the authors on semigroups of composition operators. The results are illustrated by consideration of the Hardy–Bergman space; that is, the intersection of the Hardy and Bergman Hilbert spaces on the half-plane.

Suggested Citation

  • I. Chalendar & J. R. Partington, 2023. "Composition Operators on Function Spaces on the Halfplane: Spectra and Semigroups," Springer Books, in: Ernst Albrecht & Raúl Curto & Michael Hartz & Mihai Putinar (ed.), Multivariable Operator Theory, pages 229-242, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-50535-5_10
    DOI: 10.1007/978-3-031-50535-5_10
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