On generators of C0-semigroups of composition operators

  • Eva A. Gallardo-Gutiérrez
  • Dmitry V. Yakubovich


Avicou, Chalendar and Partington proved in 2015 [5] that an (unbounded) operator Af = G·f' on the classical Hardy space generates a C0 semigroup of composition operators if and only if it generates a quasicontractive semigroup. Here we prove that if such an operator A generates a C0 semigroup, then it is automatically a semigroup of composition operators, so that the condition of quasicontractivity of the semigroup in the cited result is not necessary. Our result applies to a rather general class of Banach spaces of analytic functions in the unit disc.


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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  • Eva A. Gallardo-Gutiérrez
    • 1
    • 2
  • Dmitry V. Yakubovich
    • 3
    • 4
  1. 1.Departamento de Análisis Matemático, Facultad de MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)MadridSpain
  3. 3.Departamento de MatemáticasUniversidad Autónoma de Madrid, CantoblancoMadridSpain
  4. 4.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)MadridSpain

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