Skip to main content
SpringerLink
Log in

Points de namioka espaces normants applications à la théorie isométrique de la dualité

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

Abstract

We study in this work various aspects of the isometric theory of duality. We show that in wide classes of Banach spaces, dual spaces are characterized by the existence of a retraction fromE″ ontoE. The predual of such spaces is then unique. We study the imbedding of regularly normed spaces into dual spaces. We better the known results on loss of regularity of the norm of dual spaces. We characterize the dual norms on an Asplund space in terms of “bad differentiability”.

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

Bibliographie

  1. B. Beauzamy et B. Maurey,Points minimaux et ensembles optimaux dans les espaces de Banach, J. Functional Analysis24 (1977), 107–139.

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Bourgain, D. H. Fremlin and M. Talagrand,Pointwise compact sets of Baire-measurable functions, Amer. J. Math.100 (1978), 845–886.

    Article  MATH  MathSciNet  Google Scholar 

  3. W. J. Davis and W. J. Johnson,A renorming of nonreflexive Banach spaces, Proc. Amer. Math. Soc.37 (1973), 386–489.

    MathSciNet  Google Scholar 

  4. J. Diestel,Geometry of Banach Spaces—Selected Topics, Lecture Notes in Math.485, Springer-Verlag, 1975.

  5. J. Lindenstrauss and L. Tzafriri,Classical Banach Spaces I, Springer-Verlag, 1977.

  6. I. Namioka and R. R. Phelps,Banach spaces which are Asplund spaces, Duke Math. J.42 (1975).

  7. H. P. Rosenthal,Point-wise compact subset of the first Baire class, Amer. J. Math.99 (1977), 362–378.

    Article  MATH  MathSciNet  Google Scholar 

  8. V. L. Smulyan,Sur la dérivabilité de la norme dans l’espace de Banach, Dokl. Acad. Nauk SSSR27 (1940), 643–648.

    Google Scholar 

  9. M. Talagrand, Espaces de Banach faiblement {ie220-1}, Ann. of Math.110 (1979), 407–438.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Equipe d’Analyse, Universite Paris VI, 75230, Paris Cedex 05, France

    Gilles Godefroy

Authors
  1. Gilles Godefroy
    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

Godefroy, G. Points de namioka espaces normants applications à la théorie isométrique de la dualité. Israel J. Math. 38, 209–220 (1981). https://doi.org/10.1007/BF02760806

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02760806

Search

Navigation