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Results in Mathematics

, 74:197 | Cite as

Dynamics of the Volterra-Type Integral and Differentiation Operators on Generalized Fock Spaces

  • José BonetEmail author
  • Tesfa Mengestie
  • Mafuz Worku
Article
  • 68 Downloads

Abstract

Various dynamical properties of the differentiation and Volterra-type integral operators on generalized Fock spaces are studied. We show that the differentiation operator is always supercyclic on these spaces. We further characterize when it is hypercyclic, power bounded and uniformly mean ergodic. We prove that the operator satisfies the Ritt’s resolvent condition if and only if it is power bounded and uniformly mean ergodic. Some similar results are obtained for the Volterra-type and Hardy integral operators.

Keywords

Generalized Fock spaces power bounded uniformly mean ergodic Volterra-type integral operator differential operator Hardy operator supercyclic hypercyclic cyclic Ritt’s resolvent condition 

Mathematics Subject Classification

Primary 47B38 30H20 Secondary 46E15 47A16 47A35 

Notes

Acknowledgements

The authors are very thankful to the referee for the careful reading of our paper and many suggestions which corrected and improved our manuscript. Part of this work was done during the third-named author’s stay at the Instituto Universitario de Matemática Pura y Aplicada of the Universitat Politècnica de València. He would like to thank Prof. José Bonet, Prof. Alfred Peris and all other members of the institute for their hospitality and kindness during his stay in Valencia, Spain.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Instituto Universitario de Matemática Pura y Aplicada IUMPAUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Department of Mathematical SciencesWestern Norway University of Applied SciencesStordNorway
  3. 3.Department of MathematicsAddis Ababa UniversityAddis AbabaEthiopia

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