Hypercyclicity and chaoticity spaces of $C_0$ semigroups

Jacek Banasiak; Marcin Moszyński

doi:10.3934/dcds.2008.20.577

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2008, Volume 20, Issue 3: 577-587. Doi: 10.3934/dcds.2008.20.577

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Hypercyclicity and chaoticity spaces of $C_0$ semigroups

Jacek Banasiak^1, and
Marcin Moszyński^2,

1.
School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4000
2.
Wydział Matematyki Informatyki i Mechaniki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa

Received: February 28, 2007

Revised: July 31, 2007

Published: August 2008

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Abstract

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.

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Mathematics Subject Classification: 47A16, 47D03.

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