Skip to main content
SpringerLink
Log in

Two-Isometries and de Branges–Rovnyak Spaces

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

We characterize the symbols of the de Branges–Rovnyak spaces for which the shift operator is concave or 2-isometry. As applications, we consider wandering \(z\)-invariant subspaces and equality between a de Branges–Rovnyak space and a Dirichlet type space.

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. Baranov, A.D., Fricain, E., Mashreghi, J.: Weighted norm inequalities for de Branges–Rovnyak spaces and their applications. Am. J. Math. 132(1), 125–155 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  2. Blandignères, A., Fricain, E., Gaunard, F., Hartmann, A., Ross, W.T.: Reverse Carleson measures for de Branges–Rovnyak spaces. http://arxiv.org/abs/1308.1574

  3. Chevrot, N., Guillot, D., Ransford, T.: De Branges–Rovnyak spaces and Dirichlet spaces. J. Funct. Anal. 259, 2366–2383 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  4. Costara, C., Ransford, T.: Which de Branges–Rovnyak spaces are Dirichlet spaces (and vice versa)? J. Funct. Anal. 265, 3204–3218 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  5. El-Fallah, O., Kellay, K., Mashreghi, J., Ransford, T.: A primer on the Dirichlet Spaces. Cambridge Tracts in Mathematics 203. Cambridge University Press, Cambridge (2014)

    Google Scholar 

  6. Richter, S.: Invariant subspaces of the Dirichlet shift. J. Reine Angew. Math. 386, 205–220 (1988)

    MATH  MathSciNet  Google Scholar 

  7. Richter, S.: A representation theorem for cyclic analytic two-isometries. Trans. Am. Math. Soc. 328, 325–349 (1991)

    Article  MATH  Google Scholar 

  8. Richter, Sundberg, C.: Multipliers and invariant subspaces in the Dirichlet space. J. Oper. Theory 28, 167–186 (1992)

    MATH  MathSciNet  Google Scholar 

  9. Sarason, D.: Doubly shift-invariant spaces in \(H^2\). J. Oper. Theory 16, 75–97 (1986)

    MATH  MathSciNet  Google Scholar 

  10. Sarason, D.: Sub-Hardy Hilbert Spaces in the Unit Disk. Wiley, New York (1994)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IMB, Université de Bordeaux, 351 cours de la Liberation, 33405, Talence, France

    Karim Kellay & Mohamed Zarrabi

Authors
  1. Karim Kellay
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohamed Zarrabi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Karim Kellay.

Additional information

Communicated by Amol Sasane.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kellay, K., Zarrabi, M. Two-Isometries and de Branges–Rovnyak Spaces. Complex Anal. Oper. Theory 9, 1325–1335 (2015). https://doi.org/10.1007/s11785-014-0420-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11785-014-0420-0

Keywords

Mathematics Subject Classification

Search

Navigation