Skip to main content
SpringerLink
Log in

Proximinal subspaces of finite codimension in direct sum spaces

  • Published:
Proceedings of the Indian Academy of Sciences - Mathematical Sciences Aims and scope Submit manuscript

Abstract

We give a necessary and sufficient condition for proximinality of a closed subspace of finite codimension in c0-direct sum of Banach spaces.

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

References

  1. Garkavi A L, On the best approximation by the elements of infinite dimensional subspaces of a certain class,Mat. Sb. 62 (1963) 104–120

    MathSciNet  Google Scholar 

  2. Garkavi A L, Helley’s problem and best approximation in spaces of continuous functions,Izv. Akad. Nauk SSSR Ser. Mat. 31 (1967) 641–656

    MATH  MathSciNet  Google Scholar 

  3. Godefroy Gilles and Indumathi V, Strong proximinality and polyhedral spaces,Revista Matemática Complutense (to appear)

  4. Indumathi V, Proximinal subspaces of finite codimension in general normed linear spaces,Proc. London Math. Soc. 45(3) (1982) 435–455

    Article  MATH  MathSciNet  Google Scholar 

  5. Indumathi V, On transitivity of proximinality,J. Approx. Theory 49(2) (1987) 130–143

    Article  MATH  MathSciNet  Google Scholar 

  6. Pollul W, Reflexvitat und Existenz-Teilraume in der linearen Approximations theorie,Dissertation Bonn (1971); Schriften der Ges fur Math und Datenverarbeitung,Bonn 53 (1972) 1–21

  7. Singer Ivan, Best approximation in normed linear spaces by elements of linear subspaces, Die Grundlehren der mathematischen Wissenschaften,Band 171 (Springer Verlag) (1970)

  8. Singer Ivan, On best approximation in normed linear spaces by elements of subspaces of finite codimension,Rev. Roumaine Math. Pure. Appl. 17 (1972) 1245–1256

    MATH  Google Scholar 

  9. Vlasov L P, Elements of best approximation relative to subspaces of finite codimension,Mat. Zametki 32(3) (1982) 325–341

    MathSciNet  Google Scholar 

  10. Vlasov L P, Subspaces of finite codimension: Existence of elements of best approximation,Mat. Zametki 37(1) (1985) 78–85

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Pondicherry University, Kalpet, 605 014, Pondicherry, India

    V. Indumathi

Authors
  1. V. Indumathi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Indumathi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Indumathi, V. Proximinal subspaces of finite codimension in direct sum spaces. Proc. Indian Acad. Sci. (Math. Sci.) 111, 229–239 (2001). https://doi.org/10.1007/BF02829593

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02829593

Keywords

Search

Navigation