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Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on Lp Spaces
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In this paper, we discuss hypercyclicity, supercyclicity and cyclicity of composition operators on lp(1 ≤ p < ∞). We prove that no composition operator is hypercyclic on lp. Further, we also prove that CΦ : lp → lp is supercyclic if and only if Φ is injective and Φn has no fixed point in N, for any n ∈ N. We also give a sufficient condition and some necessary conditions for cyclicity of composition operator.
Keywords
Hypercyclicity, Supercyclicity, Cyclicity, Composition Operator on lp.
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