Advertisement

Siberian Mathematical Journal

, Volume 44, Issue 5, pp 749–756 | Cite as

On Some Isomorphism on the Category of b-Spaces

  • B. Aqzzouz
Article

Abstract

Given a nuclear b-space N, we show that if Ω is a finite or σ-finite measure space and 1≤p≤∞, then the functors Lloc p (Ω,Nε.) and NεL p (Ω,.) are isomorphic on the category of b-spaces of L. Waelbroeck.

εb-space ε-product Lp-space 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hogbe-Nlend H., Théorie des Bornologies et Applications, Springer-Verlag, Berlin; Heidelberg; New York (1971). (Lecture Notes in Math.; 213).Google Scholar
  2. 2.
    Waelbroeck L., Topological Vector Spaces and Algebras, Springer-Verlag, Berlin; Heidelberg; New York (1971). (Lecture Notes in Math.; 230).Google Scholar
  3. 3.
    Waelbroeck L., “Duality and the injective tensor product,” Math. Ann., 163, 122–126 (1966).Google Scholar
  4. 4.
    Jarchow H., Locally Convex Spaces, B. G. Teubner, Stuttgart (1981).Google Scholar
  5. 5.
    Lindenstrauss J. and Tzafriri L., Classical Banach Spaces, Springer-Verlag, Berlin (1973). (Lecture Notes in Math.; 338).Google Scholar
  6. 6.
    Kaballo W., “Lifting theorems for vector valued functions and the ?-product,” in: Proc. of the First Poderborn Conference on Functional Analysis, 1977, 27, pp. 149–166.Google Scholar
  7. 7.
    Aqzzouz B., “Généralisations du Théorème de Bartle-Graves,” C. R. Acad. Sci. Paris, 333, No. 10, 925–930 (2001).Google Scholar
  8. 8.
    Houzel C. (ed) Séminaire Banach, Springer-Verlag, Berlin; Heidelberg; New York (1972). (Lecture Note in Math.; 277).Google Scholar
  9. 9.
    Henkin G. M., “Impossibility of a uniform homeomorphism between spaces of smooth functions of one and of n variables (n ? 2),” Math. USSR-Sb., 3, 551–561 (1967).Google Scholar
  10. 10.
    Frampton J. and Tromba A., “On the classification of spaces of Hölder continuous functions,” J. Funct. Anal., 10, 336–345 (1972).Google Scholar
  11. 11.
    Diestel J. and Uhl J., Vector Measures, AMS, Providence (1985). (Math. Surveys, 15).Google Scholar
  12. 12.
    Bartle R. G. and Graves L. M., “Mappings between function spaces,” Trans. Amer. Math. Soc., 72, 400–413 (1952).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • B. Aqzzouz
    • 1
  1. 1.Universite Ibn TofailKenitraMorocco

Personalised recommendations