Skip to main content

Abstract

We understand by the term projection a bounded linear operator P which maps a normed linear space X into a sub space Y in such a manner that Py = y for all yY.

The authors were supported by the United States Air Force, Office of Scientific Research.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Daugavet, I.K.: A property of completely continuous operators in the space C, (Russian) Uspehi Mat.Nauk 18 (1963) No. 113, 157–158. MR 28 #461. (The theorem of this paper is readily extended to any T 4-space which contains no isolated points).

    Google Scholar 

  2. Golomb, M.: Optimal and nearly-optimal linear approximations, in “Approximation of Functions” edited by H.L. Garabedian, Elsevier Publ.Co. (1965), 83-100.

    Google Scholar 

  3. Isbell, J.R. and Z. Semadeni: Projection constants and spaces of continuous functions. Trans. Amer. Math. Soc. 107 (1963), 38–48.

    Article  Google Scholar 

  4. Ibeke, Y.: Generalizations of the Alaoglu theorem with applications to approximation theory, part II, Proc. Japan Acad. 44 (1968), 442–444.

    Article  Google Scholar 

  5. Cheney, E.W. and D.E. Wulbert: Existence and unicity of best approximations. Math. Scand. 24 (1969), 113–140.

    Google Scholar 

  6. Singer, I.: Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces. Ed. Acad.Repub.Soc. Romania (1967). (Rumanian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1970 Springer Basel AG

About this chapter

Cite this chapter

Cheney, E.W., Price, K. (1970). Minimal Interpolating Projections. In: Collatz, L., Meinardus, G., Unger, H., Werner, H. (eds) Iterationsverfahren Numerische Mathematik Approximationstheorie. Internationale Schriftenreihe zur Numerischen Mathematik / International Series of Numerical Mathematics / Série Internationale D’Analyse Numérique, vol 15. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5833-5_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-5833-5_14

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-5834-2

  • Online ISBN: 978-3-0348-5833-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics