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Subspaces of Frequently Hypercyclic Functions for Sequences of Composition Operators

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Abstract

In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such a criterion improves some already known special cases, and, in addition, it is also valid to provide dense vector subspaces as well as large closed ones consisting entirely, except for zero, of functions that are frequently hypercyclic.

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Acknowledgements

The first, second, and fourth authors have been partially supported by Plan Andaluz de Investigación de la Junta de Andalucía FQM-127 Grant P08-FQM-03543 and by MEC Grant MTM2015-65242-C2-1-P. The third author has been supported by DFG-Forschungsstipendium JU 3067/1-1.

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Authors and Affiliations

  1. Departamento de Análisis Matemático, Instituto de Matemáticas Antonio de Castro Brzezicki (IMUS), Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41080, Sevilla, Spain

    L. Bernal-González & M. C. Calderón-Moreno

  2. Fachbereich IV Mathematik, Universität Trier, 54286, Trier, Germany

    A. Jung

  3. Departamento de Análisis Matemático Facultad de Matemáticas, Universidad de Sevilla, Avda. Reina Mercedes s/n, 41080, Sevilla, Spain

    J. A. Prado-Bassas

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  1. L. Bernal-González
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  2. M. C. Calderón-Moreno
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  3. A. Jung
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  4. J. A. Prado-Bassas
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Corresponding author

Correspondence to J. A. Prado-Bassas.

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Communicated by Sergey Denisov.

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Bernal-González, L., Calderón-Moreno, M.C., Jung, A. et al. Subspaces of Frequently Hypercyclic Functions for Sequences of Composition Operators. Constr Approx 50, 323–339 (2019). https://doi.org/10.1007/s00365-019-09455-4

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  • DOI: https://doi.org/10.1007/s00365-019-09455-4

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