Skip to main content
SpringerLink
Log in

Smoothness indices for convex functions and the unique Hahn-Banach extension problem

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

References

  1. Cunningham, F., Jr.:L-structure inL-spaces. Trans. Amer. Math. Soc.95, 274–299 (1960).

    Google Scholar 

  2. Dunford, N., Schwartz, J.: Linear operators, part I. New York: Interscience 1958.

    Google Scholar 

  3. Fullerton, R., Braunschweiger, C.: Quasi-interior points and the extension of linear functionals. Math. Ann.162, 214–224 (1966).

    Google Scholar 

  4. Garkavi, A.: Best approximation by elements of infinite dimensional spaces of a certain class. Mat. Sbornik62, 104–120 (1963).

    Google Scholar 

  5. —: The uniqueness of solutions to theL-problem of moments. Izvestija Akad. Nauk SSSR Ser. Mat.28, 553–570 (1964).

    Google Scholar 

  6. Holmes, R.: A geometric characterization of non-atomic measure spaces. Math. Ann.182, 55–59 (1969).

    Google Scholar 

  7. Mackey, G.: Note on a theorem of Murray. Bull. Amer. Math. Soc.52, 322–325 (1946).

    Google Scholar 

  8. Moreau, J.: Etude locale d'une fonctionnelle convexe. Faculté des Sciences de Montpellier (1963).

  9. Phelps, R.: Uniqueness of Hahn-Banach extensions and unique best approximation. Trans. Amer. Math. Soc.95, 238–255 (1960).

    Google Scholar 

  10. —: Chebyshev subspaces of finite dimension inL 1. Proc. Amer. Math. Soc.17, 646–652 (1966).

    Google Scholar 

  11. Poulsen, E.: Eindeutige Hahn-Banach-Erweiterungen. Math. Ann.162, 225–227 (1966).

    Google Scholar 

  12. Pshenichnij, B.: Convex programming in a normed space. Kibernetika1, 46–54 (1965).

    Google Scholar 

  13. Weston, J.: A note on the extension of linear functionals. Amer. Math. Monthly67, 444–445 (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of Mathematical Sciences, Purdue University, 47907, Lafayette, Indiana, USA

    Richard Holmes

Authors
  1. Richard Holmes
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by a grant from the Purdue Research Foundation.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Holmes, R. Smoothness indices for convex functions and the unique Hahn-Banach extension problem. Math Z 119, 95–110 (1971). https://doi.org/10.1007/BF01109961

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01109961

Keywords

Search

Navigation