Skip to main content
SpringerLink
Log in

Disjoint and common hypercyclic algebras

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

Over time the concept of hypercyclicity has been explored in different manners and contexts, gaining new forms and applications. In particular when the space has an adjacent structure, we can always look for sets of hypercyclic vectors compatible with that framework. In this paper we deal with hypercyclic operators acting on Fréchet sequence algebras and give criteria for the existence of common and disjoint hypercyclic algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Abakumov and J. Gordon, Common hypercyclic vectors for multiples of backward shift, Journal of Functional Analysis 200 (2003), 494–504.

    Article  MathSciNet  Google Scholar 

  2. F. Bayart and E. Matheron, How to get common universal vectors, Indiana University Mathematics Journal 56 (2007), 553–580

    Article  MathSciNet  Google Scholar 

  3. F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge Tracts in Mathematics, Vol. 179, Cambridge University Press, Cambridge, 2009.

    Book  Google Scholar 

  4. F. Bayart, F. Costa Júnior and D. Papathanasiou, Baire theorem and hypercyclic algebras, Advances in Mathematics 376 (2021), Article no. 107419.

  5. L. Bernal-González, Disjoint hypercyclic operators, Studia Mathematica 182 (2007), 113–131.

    Article  MathSciNet  Google Scholar 

  6. J. Bès and A. Peris, Disjointness in hypercyclicity, Journal of Mathematical Analysis and Applications 336 (2007), 297–315.

    Article  MathSciNet  Google Scholar 

  7. J. Bès, Ö. Martin and R. Sanders, Weighted shifts and disjoint hypercyclicity, Journal of Operator Theory 72 (2014), 15–40.

    Article  MathSciNet  Google Scholar 

  8. G. Costakis and M. Sambarino, Genericity of wild holomorphic functions and common hypercyclic vectors, Advances in Mathematics 182 (2004), 278–306.

    Article  MathSciNet  Google Scholar 

  9. K.-G. Grosse-Erdmann and A. Peris, Linear Chaos, Universitext, Springer, London, 2011.

    Book  Google Scholar 

  10. C. Kitai, Invariant closed sets for linear operators, Ph.D. thesis, University of Toronto, Toronto, ON, 1982.

    Google Scholar 

  11. S. Shkarin, On the set of hypercyclic vectors for the differentiation operator, Israel Journal of Mathematics 180 (2010), 271–283.

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgement

We thank the referee for their very careful reading of the paper which lead to several significant improvements.

Author information

Authors and Affiliations

  1. Laboratoire de Mathématiques Blaise Pascal UMR 6620 CNRS, Université Clermont Auvergne, Campus universitaire des Cézeaux, 3 place Vasarely, 63178, Aubière Cedex, France

    Frédéric Bayart, Fernando Costa Jr. & Dimitris Papathanasiou

Authors
  1. Frédéric Bayart
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fernando Costa Jr.
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dimitris Papathanasiou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Frédéric Bayart.

Additional information

The first and the second author were partially supported by the grant ANR-17-CE40-0021 of the French National Research Agency ANR (project Front).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bayart, F., Costa, F. & Papathanasiou, D. Disjoint and common hypercyclic algebras. Isr. J. Math. 250, 211–264 (2022). https://doi.org/10.1007/s11856-022-2337-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-022-2337-z

Search

Navigation