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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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- Ansari, I. S., Hypercyclic and Cyclic Vectors, J. Funct. Anal., 128 (1995), 374-383.
- Ansari, I. S., Bourdon, S. P., Some properties of cyclic operators, Acta Sci. Math.(Szeged), 63 (1997), 195-207.
- Bayart, F., Matheron, E., Dynamics of Linear Operators, Cambridge University Press, 2009.
- Birkhoff, D. G., Demonstration dun theoreme sur les fonctions entieres, C. R. Acad. Sci. Paris, 189 (1929), 473-475.
- Bourdon, S. P, Invariant manifold of hypercyclic vectors, Proc. Amer. Math. Soc., 118 (1993), 845-847.
- Grosse-Erdmann, G. K., Manguillot, P. A., Linear Chaos, Springer-Verlag London Limited, 2011.
- MacLane, R. G., Sequences of derivatives and normal families , J. Analyse Math., 2 (1952/53), 72-87.
- Rolewicz, S., On orbits of element, Studia Math., 32 (1969), 17-22.
- Shapiro, H. J., Composition operators and classical function theory, Springer-Verlag, 1993.
- Singh, K. R., Manhas, S. J., Composition Operators on Function Spaces, North-Holland, NewYork, 1993.
- Singh, L., A study of composition operators on l2, Thesis, Banaras Hindu University, Varanasi, 1987.
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