Skip to main content
SpringerLink
Log in

Injective spaces of real-valued functions with the baire property

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

Abstract

Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.

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. D. Amir,Continuous function spaces with the bounded extension property, Bulletin of the Research council of Israel, Section F10F (1962), 133–138.

    MathSciNet  Google Scholar 

  2. D. Amir,Projections onto continuous function spaces, Proceedings of the American Mathematical Society15 (1964), 396–402.

    Article  MATH  MathSciNet  Google Scholar 

  3. S. A. Argyros,On the space of bounded measurable functions, The Quarterly Journal of Mathematics. Oxford34 (1983), 129–132.

    Article  MATH  Google Scholar 

  4. R. Engelking,General Topology, Heldermann Verlag, Berlin, 1989.

    MATH  Google Scholar 

  5. D. H. Fremlin,Measure Additive Coverings and Measurable Selectors, Dissertationes Mathematicae CCLX, Warszawa, 1987.

  6. J. R. Isbell and Z. Semadeni,Projection constants and spaces of continuous functions, Transactions of the American Mathematical Society107 (1963), 38–48.

    Article  MATH  MathSciNet  Google Scholar 

  7. K. Kuratowski,Topology, Vol. I, Academic Press, New York and London, 1966.

    Google Scholar 

  8. A. Pełczyński and V. N. Sudakov,Remark on non-complemented subspaces of the space m(S), Colloquium MathematicumIX (1962), 85–88.

    Google Scholar 

  9. R. S. Philips,On linear transformations, Transactions of the American Mathematical Society48 (1940), 516–541.

    Article  MathSciNet  Google Scholar 

  10. J. Wolfe,Injective Banach spaces of type C(T), Israel Journal of Mathematics18 (1974), 133–140.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Wolfe,Injective Banach spaces of continuous functions, Transactions of the American Mathematical Society235 (1978), 116–139.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departmento de Análisis Matemático, Universidad de Valencia, Dr. Moliner 50, 46100, Burjasot (Valencia), Spain

    José L. Blasco & C. Ivorra

Authors
  1. José L. Blasco
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Ivorra
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blasco, J.L., Ivorra, C. Injective spaces of real-valued functions with the baire property. Israel J. Math. 91, 341–348 (1995). https://doi.org/10.1007/BF02761655

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02761655

Keywords

Search

Navigation