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

I. Chalendar () and J. R. Partington ()
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I. Chalendar: Université Gustave Eiffe, LAMA, (UMR 8050), UPEM, UPEC, CNRS
J. R. Partington: University of Leeds, School of Mathematics

A chapter in Multivariable Operator Theory, 2023, pp 229-242 from Springer

Abstract: 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.

Keywords: Composition operator; Hardy space; Bergman space; Spectrum; Essential spectrum; Operator semigroup; 30H10; 30H20; 47B33; 47D03 (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-50535-5_10

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DOI: 10.1007/978-3-031-50535-5_10

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