Collectanea Mathematica

, Volume 67, Issue 3, pp 347–356 | Cite as

Disjoint hypercyclic weighted translations generated by aperiodic elements

Article

Abstract

In this paper, we give a characterization for the disjoint hypercyclicity of finite weighted translations sharing the same translation part generated by an aperiodic element acting on \(L^p(G)\) with \(G\) a locally compact group and \(1\le p<\infty \).

Keywords

Hypercyclicity Weighted translation Locally compact group \(L^p\)-space 

Mathematics Subject Classification

Primary 47A16 Secondary 44A35 43A15 

References

  1. 1.
    Bernal-González, L.: Disjoint hypercyclic operators. Studia Math. 2, 113–131 (2007)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bayart, F., Matheron, E.: Dynamics of Linear Operators. Cambridge University Press, Cambridge (2009)Google Scholar
  3. 3.
    Bès, J., Martin, Ö.: Compositional disjoint hypercyclicity equals disjoint supercyclicity. Houston J. Math. 38, 1149–1163 (2012)MathSciNetMATHGoogle Scholar
  4. 4.
    Bès, J., Martin, Ö., Peris, A.: Disjoint hypercyclic linear fractional composition operators. J. Math. Appl. 381, 843–856 (2011)MathSciNetMATHGoogle Scholar
  5. 5.
    Bès, J., Martin, Ö., Peris, A., Shakarin, R.: Disjoint mixing operators. J. Funct. Anal. 263, 1283–1322 (2012)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Bès, J., Martin, Ö., Sanders, R.: Weighted shifts and disjoint hypercyclicity. J. Oper. Theory (preprint)Google Scholar
  7. 7.
    Bés, J., Peris, A.: Disjointness in hypercyclicity. J. Math. Anal. Appl. 336, 297–315 (2007)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Chen, C.C.: Chaotic weighted translations on groups. Arch. Math. 97, 61–68 (2011)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Chen, C.C.: Supercyclic and cesàro hypercyclic weighted transaltions on groups. Taiwanese J. Math. 16, 1815–1827 (2012)MathSciNetMATHGoogle Scholar
  10. 10.
    Chen, C.C.: Hypercyclic weighted translations generated by non-torsion elements. Arch. Math. 101, 135–141 (2013)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Chen, C.C., Chu, C.H.: Hypercyclicity of weighted convolution operators on homogeneous spaces. Proc. Am. Math. Soc. 137, 2709–2781 (2009)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Chen, C.C., Chu, C.H.: Hypercyclic weighted translations on groups. Proc. Am. Math. Soc. 139, 2839–2846 (2011)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Grosse-Erdmann, K.G., Manguillot, A.P.: Linear Chaos. Springer, New York (2011)CrossRefMATHGoogle Scholar
  14. 14.
    Grosser, S., Moskowitz, M.: On central topological groups. Trans. Am. Math. Soc. 127, 317–340 (1967)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Hewitt, E., Ross, K.A.: Abstract Harmonic Analysis. Springer, Heidelberg (1979)MATHGoogle Scholar
  16. 16.
    Martin, Ö.: Disjoint hypercyclic and supercyclic composition operators, PhD thesis, Bowling Green State University (2011)Google Scholar
  17. 17.
    Salas, H.: Dual disjoint hypercyclic weighted shifts. J. Math. Anal. Appl. 374(1), 106–117 (2011)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Salas, H.: The strong disjoint blow-up/collapse property. J. Funct. Spaces Appl. Art. ID 146517 (2013)Google Scholar
  19. 19.
    Shkarin, S.: A short proof of existence of disjoint hypercyclic operators. J. Math. Anal. Appl. 367, 713–715 (2010)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Sanders, R., Shkarin, S.: Existence of disjoint weakly mixing operators that fail to satisfy the Disjoint Hypercyclicity Criterion. J. Math. Anal. Appl. 417, 834–855 (2014)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Universitat de Barcelona 2015

Authors and Affiliations

  1. 1.Department of MathematicsTianjin UniversityTianjinPeople’s Republic of China
  2. 2.School of Mathematical SciencesTianjin Normal UniversityTianjinPeople’s Republic of China

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