Skip to main content
SpringerLink
Log in

The polynomial Daugavet property for atomless L 1(μ)-spaces

  • Published:
Archiv der Mathematik Aims and scope Submit manuscript

Abstract

For any atomless positive measure μ, the space L 1(μ) has the polynomial Daugavet property, i.e., every weakly compact continuous polynomial \({P:L_1(\mu)\longrightarrow L_1(\mu)}\) satisfies the Daugavet equation \({\|{\rm Id} + P\|=1 + \|P\|}\). The same is true for the vector-valued spaces L 1(μ, E), μ atomless, E arbitrary.

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. Yu. A. Abramovich and C. D. Aliprantis, An Invitation to Operator Theory, Graduate Studies in Math. 50, Amer. Math. Soc., Providence, Rhode Island, (2002).

  2. F. Albiac and N. J. Kalton, Topics in Banach space theory, Graduate Texts in Mathematics 233, Springer-Verlag, New York, (2006).

  3. Choi Y.S. et al.: The Daugavet equation for polynomials. Studia Math. 178, 63–84 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Choi Y.S. et al.: The polynomial numerical index for some complex vector-valued function spaces. Quart. J. Math. 59, 455–474 (2008)

    Article  MATH  Google Scholar 

  5. I. K. Daugavet, On a property of completely continuous operators in the space C, Uspekhi Mat. Nauk 18 (1963), 157–158 (Russian).

    Google Scholar 

  6. S. Dineen, Complex Analysis on Infinite Dimensional Spaces, Graduate Studies in Math. 50, Amer. Math. Soc., Providence, Rhode Island (2002).

  7. Kadets V.M. et al.: Banach spaces with the Daugavet property. Trans. Amer. Math. Soc. 352, 855–873 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  8. Werner D.: Recent progress on the Daugavet property. Irish Math. Soc. Bull. 46, 77–97 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Miguel Martín & Javier Merí

  2. Department of Mathematics, Chernivtsi National University, str. Kotsyubyns’koho 2, Chernivtsi, 58012, Ukraine

    Mikhail Popov

Authors
  1. Miguel Martín
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Javier Merí
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mikhail Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel Martín.

Additional information

First and second authors partially supported by Spanish MEC and FEDER project no. MTM2006-04837 and Junta de Andalucía and FEDER grants FQM-185 and P06-FQM-01438. Third author partially supported by Ukr. Derzh. Tema N 0103Y001103 and Junta de Andalucía and FEDER grant P06-FQM-01438.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martín, M., Merí, J. & Popov, M. The polynomial Daugavet property for atomless L 1(μ)-spaces. Arch. Math. 94, 383–389 (2010). https://doi.org/10.1007/s00013-010-0105-5

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00013-010-0105-5

Mathematics Subject Classification (2000)

Keywords

Search

Navigation