Skip to main content
Log in

Potentials and isometric embeddings inL 1

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

Abstract

lp/3 does not embed isometrically inL 1, forp>2. The question whenl nr embeds isometrically inL pis completely answered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

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. E. D. Bolker,A class of convex bodies, Trans. Amer. Math. Soc.145 (1969), 323–345.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Bretagnolle, D. Dacunha-Castelle and J.-L. Krivine,Lois stables et espaces L p, Ann. Inst. H. Poincaré2 (1966), 231–259.

    MathSciNet  Google Scholar 

  3. R. V. Chacon,Potential functions and martingales (to appear).

  4. A. Grothendieck,Résumé de la théorie métrique des produits tensoriels topologiques, Bol. Soc. Mat. São Paulo8 (1953), 1–79.

    MathSciNet  Google Scholar 

  5. C. Herz,A class of negative definite functions, Proc. Amer. Math. Soc.14 (1963), 670–676.

    Article  MATH  MathSciNet  Google Scholar 

  6. J. Lindenstrauss,On the extension of operators with a finite-dimensional range, Illinois J. Math.8 (1964), 488–499.

    MATH  MathSciNet  Google Scholar 

  7. J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces, Lecture Notes in Mathematics 338, Springer Verlag, 1973.

  8. R. Loève,Probability Theory, Princeton, D. Van Nostrand, 1963.

  9. H. L. Royden,Real Analysis, McMillan, 1967.

  10. R. Schneider,Zonoids whose polars are zonoids, Proc. Amer. Math. Soc.50 (1975), 365–368.

    Article  MATH  MathSciNet  Google Scholar 

  11. H. S. Witsenhausen,Metric inequalities and the zonoid problem, Proc. Amer. Math. Soc.40 (1973), 517–520.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dor, L.E. Potentials and isometric embeddings inL 1 . Israel J. Math. 24, 260–268 (1976). https://doi.org/10.1007/BF02834756

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02834756

Keywords

Navigation