Hypercyclicity, Supercyclicity And Cyclicity Of Composition Operators On Lp Spaces

Jump To References Section

Authors

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

DOI:

https://doi.org/10.18311/jims/2019/22578

Keywords:

Hypercyclicity, Supercyclicity, Cyclicity, Composition Operator on lp

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 : 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.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Downloads

Published

2018-12-12

How to Cite

Srivastava, V. K., & Chandra, H. (2018). Hypercyclicity, Supercyclicity And Cyclicity Of Composition Operators On L<sup>p</sup> Spaces. The Journal of the Indian Mathematical Society, 86(1-2), 187–198. https://doi.org/10.18311/jims/2019/22578

Issue

Volume 86, Issue 1-2, January-June 2019

Section

Articles

License

Copyright (c) 2018 Vijay Kumar Srivastava, Harish Chandra

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Crossref
Scopus
Google Scholar
Europe PMC

 

References

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.