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Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on Lp Spaces


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1 Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, India
     

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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 : lplp 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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  • Hypercyclicity, Supercyclicity and Cyclicity of Composition Operators on Lp Spaces

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Authors

Vijay Kumar Srivastava
Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, India
Harish Chandra
Department of Mathematics, Institute of Science Banaras Hindu University, Varanasi -221005, India

Abstract


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 : lplp 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.

References