Abstract
In this chapter we discuss the spectral properties of hypercyclic and chaotic operators. We obtain, in particular, Kitai’s theorem that each connected component of the spectrum of a hypercyclic operator meets the unit circle. As an application we derive properties that preclude hypercyclicity or chaos, and we obtain classes of operators that do not contain any hypercyclic operator.
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© 2011 Springer-Verlag London Limited
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Grosse-Erdmann, KG., Peris Manguillot, A. (2011). Necessary conditions for hypercyclicity and chaos. In: Linear Chaos. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-2170-1_5
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DOI: https://doi.org/10.1007/978-1-4471-2170-1_5
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2169-5
Online ISBN: 978-1-4471-2170-1
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