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On generators of C0-semigroups of composition operators

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Abstract

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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Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias No 3, 28040, Madrid, Spain

    Eva A. Gallardo-Gutiérrez

  2. Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Madrid, Spain

    Eva A. Gallardo-Gutiérrez & Dmitry V. Yakubovich

  3. Departamento de Matemáticas, Universidad Autónoma de Madrid, Cantoblanco, 28049, Madrid, Spain

    Dmitry V. Yakubovich

Authors
  1. Eva A. Gallardo-Gutiérrez
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  2. Dmitry V. Yakubovich
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Corresponding author

Correspondence to Eva A. Gallardo-Gutiérrez.

Additional information

Partially supported by Plan Nacional I+D grant no. MTM2016-77710-P, Spain.

Partially supported by Plan Nacional I+D grant no. MTM2015-66157-C2-1-P. Both authors also acknowledge the support by the ICMAT Severo Ochoa project SEV-2015-0554 of the Ministry of Economy and Competitiveness of Spain and by the European Regional Development Fund.

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Gallardo-Gutiérrez, E.A., Yakubovich, D.V. On generators of C0-semigroups of composition operators. Isr. J. Math. 229, 487–500 (2019). https://doi.org/10.1007/s11856-018-1815-9

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  • DOI: https://doi.org/10.1007/s11856-018-1815-9

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