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International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 514370, 5 pages
http://dx.doi.org/10.1155/2011/514370
Research Article

Weighted Composition Operators and Supercyclicity Criterion

1Department of Mathematics, Payame Noor University, P.O. Box: 71955-1368 Shiraz, Iran
2Department of Mathematics, Payame Noor University, P.O. Box: 19395-4697 Tehran, Iran

Received 16 April 2011; Revised 6 June 2011; Accepted 15 June 2011

Academic Editor: Naseer Shahzad

Copyright © 2011 Bahmann Yousefi and Javad Izadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Bayart and E. Matheron, Dynamics of Linear Operators, vol. 179 of Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge, UK, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. T. Bermúdez, A. Bonilla, and A. Peris, “On hypercyclicity and supercyclicity criteria,” Bulletin of the Australian Mathematical Society, vol. 70, no. 1, pp. 45–54, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. R. M. Gethner and J. H. Shapiro, “Universal vectors for operators on spaces of holomorphic functions,” Proceedings of the American Mathematical Society, vol. 100, no. 2, pp. 281–288, 1987. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. Godefroy and J. H. Shapiro, “Operators with dense, invariant, cyclic vector manifolds,” Journal of Functional Analysis, vol. 98, no. 2, pp. 229–269, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. K.-G. Große-Erdmann, “Holomorphe Monster und universelle Funktionen,” Mitteilungen aus dem Mathematischen Seminar Giessen, no. 176, pp. 1–84, 1987. View at Google Scholar
  6. D. A. Herrero, “Limits of hypercyclic and supercyclic operators,” Journal of Functional Analysis, vol. 99, no. 1, pp. 179–190, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. H. N. Salas, “Supercyclicity and weighted shifts,” Studia Mathematica, vol. 135, no. 1, pp. 55–75, 1999. View at Google Scholar · View at Zentralblatt MATH
  8. S. Yarmahmoodi, K. Hedayatian, and B. Yousefi, “Supercyclicity and hypercyclicity of an isometry plus a nilpotent,” Abstract and Applied Analysis, vol. 2011, Article ID 686832, 11 pages, 2011. View at Google Scholar
  9. B. Yousefi and H. Rezaei, “Some necessary and sufficient conditions for hypercyclicity criterion,” Proceedings of the Indian Academy of Sciences, vol. 115, no. 2, pp. 209–216, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. B. Yousefi and A. Farrokhinia, “On the hereditarily hypercyclic operators,” Journal of the Korean Mathematical Society, vol. 43, no. 6, pp. 1219–1229, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. B. Yousefi, H. Rezaei, and J. Doroodgar, “Supercyclicity in the operator algebra using Hilbert-Schmidt operators,” Rendiconti del Circolo Matematico di Palermo II, vol. 56, no. 1, pp. 33–42, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. B. Yousefi and H. Rezaei, “Hypercyclic property of weighted composition operators,” Proceedings of the American Mathematical Society, vol. 135, no. 10, pp. 3263–3271, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. B. Yousefi and S. Haghkhah, “Hypercyclicity of special operators on Hilbert function spaces,” Czechoslovak Mathematical Journal, vol. 57(132), no. 3, pp. 1035–1041, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. B. Yousefi and H. Rezaei, “On the supercyclicity and hypercyclicity of the operator algebra,” Acta Mathematica Sinica, vol. 24, no. 7, pp. 1221–1232, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. B. Yousefi and R. Soltani, “Hypercyclicity of the adjoint of weighted composition operators,” Proceedings of the Indian Academy of Sciences, vol. 119, no. 4, pp. 513–519, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. B. Yousefi, “Hereditarily transitive tuples,” to appear in Rendiconti del Circolo Matematico di Palermo. View at Publisher · View at Google Scholar · View at Zentralblatt MATH