Linear Chaos pp 137-160 | Cite as

Necessary conditions for hypercyclicity and chaos

Part of the Universitext book series (UTX)


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.


Banach Space Compact Operator Complex Hilbert Space Complex Banach Space Volterra Operator 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Karl-G. Grosse-Erdmann
    • 1
  • Alfred Peris Manguillot
    • 2
  1. 1.Institut de MathématiqueUniversité de MonsMonsBelgium
  2. 2.Institut Universitari de Matemàtica Pura i AplicadaUniversitat Politècnica de ValènciaValènciaSpain

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