Skip to main content
SpringerLink
Log in

A continuity criterion for metric projections in banach spaces

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

Abstract

The paper provides the complete characteristics of the class of reflexive strictly convex spaces in which the metric projections on each convex closed set are continuous.

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

Literature cited

  1. N. V. Efimov and S. B. Stechkin, “Certain properties of Chebyshev sets,” Dokl. Akad. Nauk SSSR, 118, No. 1, 17–19 (1958).

    Google Scholar 

  2. M. M. Day, Normed Linear Spaces [Russian translation], Moscow (1961),

  3. V. L. Klee, “Convexity of Chebyshev sets,” Math. Ann., 142, No. 3, 292–304 (1961).

    Google Scholar 

  4. Fan Ky and J. Glicksberg, “Some geometric properties of the spheres in a normed linear space,” Duke Math. J.,25, No. 4, 553–568 (1958).

    Google Scholar 

  5. E. V. Oshman, “On the continuity of metric projections in Banach spaces,” Matem. Sb.,80, No. 2, 181–194 (1969).

    Google Scholar 

  6. B. Brosowski, K. H. Hoffman, E. Schäfer, and H. Weber, “Stetigkeitssätze für metrische Projektionen. I. Metrische Projektionen auf lineare Teilräume von Co [Q, H],” Max Planck-Institut,18 (1969).

  7. B. Brosowski, K. H. Hoffman, E. Schäfer, and J. Wener, “Stetigkeitssätze für metrische Projektionen. II. (P)-Raüme und ZS Stetigkeit der metrischen Projektion,” Max Planck-Institut,19 (1969).

  8. B. Brosowski, K. H. Hoffman, E. Schäfer, and H. Weber, “Stetigkeitssätze für metrische Projektionen. III. Eine Fixpunkteigenschaft der metrischen Projektion,” Max Planck-Institut,12 (1969).

  9. B. Brosowski, K. H. Hoffman, E. Schäfer, and H. Weber, “Stetigkeitssätze für metrische Projektionen. IV. Eine hinreichende Bedingung für die φn-Stetigkeit der metrischen Projektion,” Max Planck-Institut,20 (1969).

  10. I. Singer, “Some remarks on approximative compactness,” Rev. Roumaine Math. pures et appl.,9, No. 2, 167–177 (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. A. M. Gor'kii Ural State University, USSR

    E. V. Oshman

Authors
  1. E. V. Oshman
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 459–468, October, 1971.

The author wishes to thank S. B. Stechkin for useful comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Oshman, E.V. A continuity criterion for metric projections in banach spaces. Mathematical Notes of the Academy of Sciences of the USSR 10, 697–701 (1971). https://doi.org/10.1007/BF01106468

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01106468

Keywords

Search

Navigation