Necessary conditions for hypercyclicity and chaos
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.
KeywordsBanach Space Compact Operator Complex Hilbert Space Complex Banach Space Volterra Operator
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