Skip to main content
SpringerLink
Log in

On the Orlicz function spacesL M (0, ∞)

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

Abstract

The isomorphic properties of the Orlicz function spacesL M (0, ∞) are investigated. Especially we treat the question, whether theL p-spaces are the only symmetric function spaces on (0, ∞), which are isomorphic to a symmetric function space on (0, 1). For the class of slowly varying Orlicz functions we answer this in the affirmative, and we also prove some results concerning the general case, which indicate, that it might be true there also.

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.

Similar content being viewed by others

References

  1. C. Bessaga and A. Pelczyński,On bases and absolute convergence of series in Banach spaces, Studia Math.17 (1958), 151–164.

    MATH  MathSciNet  Google Scholar 

  2. J. Bretagnolle and D. Dacunha-Castelle,Applications de l’étude de certaines formes linéaires aléatoires au plongement d’espaces de Banach dans des espaces L p, Ann. École Normale Supérieure2 (1969), 437–480.

    MATH  MathSciNet  Google Scholar 

  3. I. Kadec and A. Pelczyński,Bases, lacunary sequences and complemented subspaces in the spaces L p, Studia Math.21 (1962), 161–176.

    MATH  MathSciNet  Google Scholar 

  4. K. Lindberg,On subspaces of Orlicz sequence spaces, Studia Math.45 (1973), 119–146.

    MATH  MathSciNet  Google Scholar 

  5. J. Lindenstrauss and L. Tzafriri,Classical Banach spaces, Springer Lecture Notes, series 338, 1973.

  6. J. Lindenstrauss and L. Tzafriri,On Orlicz sequence spaces, Israel J. Math.10 (1971), 379–390.

    MATH  MathSciNet  Google Scholar 

  7. J. Lindenstrauss and L. Tzafriri,On Orlicz sequence spaces II, Israel J. Math.11 (1972), 355–379.

    MATH  MathSciNet  Google Scholar 

  8. J. Lindenstrauss and L. Tzafriri,On Orlicz sequence spaces III, Israel J. Math.14 (1973), 368–389.

    MATH  MathSciNet  Google Scholar 

  9. W. A. J. Luxemburg,Banach function spaces, Thesis, Van Gorcum Assen, Holland, 1955.

    MATH  Google Scholar 

  10. B. S. Mityagin,The homotopy structure of the general linear group of a Banach space, Russian Math. Surveys25 (1970), 54–103.

    Article  Google Scholar 

  11. A. Pelczyński and H. P. Rosenthal,Localization principles in L p-spaces (to appear).

  12. D. Dacunha-Castelle,Plongement d’espaces d’Orlicz de fonctions dans des espaces d’Orlicz de fonctions (to appear).

  13. D. Dacunha-Castelle and M. Schreiber,Techniques probabilistes pour l’étude de problèmes d’isomorphismes entre espaces de Banach (to appear).

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Odense University, Odense, Denmark

    Niels Jørgen Nielsen

Authors
  1. Niels Jørgen Nielsen
    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

Nielsen, N.J. On the Orlicz function spacesL M (0, ∞). Israel J. Math. 20, 237–259 (1975). https://doi.org/10.1007/BF02760330

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760330

Keywords

Search

Navigation