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Hypercyclicity and chaoticity spaces of $C_0$ semigroups

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  • In [10] the author provided a generalization of the classical Desch-Schappacher-Webb sufficient criterion which ensures hypercyclicity of linear semigroups. In this paper we simplify assumptions of [10], obtaining new criteria for hypercyclicity of a $C_0$ semigroup in a subspace (sub-hypercyclicity), and also for its sub-chaoticity. Moreover, we provide full characterization of chaoticity and hypercyclicity spaces of semigroups satisfying the assumptions of these new criteria. We also present examples showing that, in general, these assumptions cannot be weakened.
    Mathematics Subject Classification: 47A16, 47D03.


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