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Hypercyclicity and supercyclicity of unbounded operators

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Abstract

We study hypercyclicity and supercyclicity of unbounded operators with special focus on generators of composition \(C_0\)-semigroups and give conditions under which they are supercyclic and non-supercyclic. Further, we show that if A is a closed range operator with \(0 \in \sigma (A)\), then the sufficient conditions of the continuous version of Godefroy and Shapiro’s Criterion, which is given in Mourchid (Semigroup Forum 73:313–316, 2006) for hypercyclicity, are necessary as well.

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Acknowledgements

The author is grateful to the reviewers for their comments and suggestions that helped in greatly improving this paper. The author thanks Prof. Sachi Srivastava, University of Delhi, India, for her useful discussion in this area.

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Authors and Affiliations

  1. Department of Mathematics, H.N.B. Garhwal University, Srinagar (Garhwal), 246174, Srinagar, India

    Abhay Kumar

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  1. Abhay Kumar
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Correspondence to Abhay Kumar.

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Communicated by Enrique A. Sanchez Perez.

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Kumar, A. Hypercyclicity and supercyclicity of unbounded operators. Adv. Oper. Theory 7, 45 (2022). https://doi.org/10.1007/s43036-022-00210-4

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  • DOI: https://doi.org/10.1007/s43036-022-00210-4

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