Skip to main content
Log in

Une Caracterisation Volumique de Certains Espaces Normes de Dimension Finie

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

Abstract

We give a geometric characterization of finite dimensional normed spacesE, with a 1-unconditional basis, such that their volumetric product is minimal.

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

Bibliographie

  1. W. Blaschke,Vorlesungen über Differential Geometrie II, Springer, Berlin, 1923.

    Google Scholar 

  2. J. Bourgain et V. Milman,On Mahler’s conjecture on the volume of a convex symmetric body and its polar, preprint.

  3. O. Hanner,Intersections of translates of convex bodies, Math. Scand.4 (1956), 65–87.

    MATH  MathSciNet  Google Scholar 

  4. A. B. Hansen et A. Lima,The structure of finite dimensional Banach spaces with the 3–2 intersection property, Acta Math.46 (1981), 1–23.

    Article  MathSciNet  Google Scholar 

  5. K. Mahler,Ein Übertragungsprizip für konvexe Körper, Casopis Pest Math. Fys.68 (1939), 93–102.

    MathSciNet  Google Scholar 

  6. S. Reisner,Random polytopes and the volume-product of symmetric convex bodies, Math. Scand.58 (1986).

  7. S. Reisner,Zonoids with minimal volume-product, Math. Z., to appear.

  8. J. Saint-Raymond,Sur les volumes des corps convexes symétriques, Sem. d’Initiation à l’Analyse, 20e année (1980–81), no 11, 25 p.

  9. L. A. Santalo,Un invariante afin para los cuerpos convexos del espacio de n dimensiones, Portugal Math.8 (1949), 155–161.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meyer, M. Une Caracterisation Volumique de Certains Espaces Normes de Dimension Finie. Israel J. Math. 55, 317–326 (1986). https://doi.org/10.1007/BF02765029

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02765029

Navigation