Skip to main content
SpringerLink
Log in

Path connected components of the space of Volterra-type integral operators

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

We study the topological structure of the space of Volterra-type integral operators on Fock spaces endowed with the operator norm. We prove that the space has the same connected and path connected components which is the set of all those compact integral operators acting on the spaces. We also obtain a characterization of isolated points of the space of the operators and show that there exists no essentially isolated Volterra-type integral operator.

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. A. Aleman and A. Siskakis, An integral operator on \(H^p\), Complex Variables 28 (1995), 149–158.

    MathSciNet  MATH  Google Scholar 

  2. A. Aleman and A. Siskakis, Integration operators on Bergman spaces, Indiana Univ. Math. J. 46 (1997), 337–356.

    Article  MathSciNet  MATH  Google Scholar 

  3. O. Constantin, Volterra type integration operators on Fock spaces, Proc. Amer. Math. Soc. 140 (2012), 4247–4257.

    Article  MathSciNet  MATH  Google Scholar 

  4. O. Constantin and José Ángel Peláez, Integral operators, embedding theorems and a Littlewood–Paley formula on weighted Fock spaces, J. Geom. Anal. (2015), 1–46.

  5. T. Mengestie, Generalized Volterra companion operators on Fock spaces, Potential Anal. 44 (2016), 579–599.

    Article  MathSciNet  MATH  Google Scholar 

  6. T. Mengestie, Product of Volterra type integral and composition operators on weighted Fock spaces, J. Geom. Anal. 24 (2014), 740–755.

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Mengestie, On the spectrum of Volterra-type integral operators on Fock–Sobolev spaces, Complex Anal. Oper. Theory 11 (2017), 1451–1461.

    Article  MathSciNet  MATH  Google Scholar 

  8. T. Mengestie and M. Worku, Topological structures of generalized Volterra-type integral operators, Mediterr. J. Math. 15 (2018), 16 (Art. 42).

  9. T. Mengestie, Spectral properties of Volterra-type integral operatos on Fock–Sobolev spaces, J. Korean Math. Soc. 54 (2017), 1801–1816.

    MathSciNet  Google Scholar 

  10. J. Pau and J. A. Peláez, Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights. J. Funct. Anal. 259 (2010), 2727–2756.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. Pau and J. A. Peláez, Volterra type operators on Bergman spaces with exponential weights, Contemp. Math.  561 (2012), 239–252.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. Pau, Integration operators between Hardy spaces of the unit ball of \(\mathbb{C}^n\), J. Funct. Anal. 270 (2016), 134–176.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Western Norway University of Applied Sciences, Klingenbergvegen 8, 5414, Stord, Norway

    Tesfa Mengestie

Authors
  1. Tesfa Mengestie
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tesfa Mengestie.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mengestie, T. Path connected components of the space of Volterra-type integral operators. Arch. Math. 111, 389–398 (2018). https://doi.org/10.1007/s00013-018-1193-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-018-1193-x

Keywords

Mathematics Subject Classification

Search

Navigation