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On the Recurrent C0-Semigroups, Their Existence, and Some Criteria

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  • Mansooreh Moosapoor
  • Tuncer Acar

Abstract

In this paper, recurrent C0-semigroups are introduced and investigated. It is proved that, despite hypercyclic C0-semigroups, recurrent C0-semigroups can be found on finite-dimensional Banach spaces. Some criteria are stated for recurrence, which is based on open sets, neighborhoods of zero, and special eigenvectors. It is established that having a dense set of recurrent vectors is a sufficient and necessary condition for a C0-semigroup to be recurrent. Moreover, the direct sum of recurrent C0-semigroups is investigated.

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  • Mansooreh Moosapoor & Tuncer Acar, 2021. "On the Recurrent C0-Semigroups, Their Existence, and Some Criteria," Journal of Mathematics, Hindawi, vol. 2021, pages 1-7, September.
    • Handle: RePEc:hin:jjmath:6756908
    DOI: 10.1155/2021/6756908
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