Skip to main content
SpringerLink
Log in

Finite Blaschke product and the multiplication operators on Sobolev disk algebra

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

Let R(D) be the algebra generated in Sobolev space W 22(D) by the rational functions with poles outside the unit disk \( \overline D \). In this paper the multiplication operators M g on R(D) is studied and it is proved that M g ∼ \( M_{z^n } \) if and only if g is an n-Blaschke product. Furthermore, if g is an n-Blaschke product, then M g has uncountably many Banach reducing subspaces if and only if n > 1.

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. Jiang C L, Wang Z Y. Structure of Hilbert Space Operators. Singapore: World Scientific, 2006

    MATH  Google Scholar 

  2. Liu Y Q, Wang Z Y. The commutant of multiplication operators on Sobolev disk algebra. J Anal Appl, 2: 65–86 (2004)

    MATH  MathSciNet  Google Scholar 

  3. Wang Z Y, Liu Y Q. The multiplication operators on Sobolev disk algebra. Sci China Ser A-Math, 48: 1395–1401 (2005)

    Article  MATH  Google Scholar 

  4. Conway J B. Functions of One Complex Variable II. GTM 159. New York: Springe-Verlag, 1995

    Google Scholar 

  5. Garnett J B. Bounded Analytic Functions. New York: Academic Press, 1981

    MATH  Google Scholar 

  6. Jiang C L, Wang Z Y. Strongly irreducible operators on Hilbert space. π-Pitman Research Notes in Mathematics Series 389. Longman, 1998

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, China

    ZongYao Wang, RuiFang Zhao & YongFei Jin

Authors
  1. ZongYao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. RuiFang Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. YongFei Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to ZongYao Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 10471041)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, Z., Zhao, R. & Jin, Y. Finite Blaschke product and the multiplication operators on Sobolev disk algebra. Sci. China Ser. A-Math. 52, 142–146 (2009). https://doi.org/10.1007/s11425-008-0051-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-008-0051-x

Keywords

MSC(2000)

Search

Navigation