Skip to main content
Log in

The Representation Theorem of onto Isometric Mappings between Two Unit Spheres of l 1(Γ) Type Spaces and The Application to the Isometric Extension Problem

  • ORIGINAL ARTICLES
  • Published:
Acta Mathematica Sinica Aims and scope Submit manuscript

Abstract

In this paper, we .rst derive the representation theorem of onto isometric mappings in the unit spheres of l 1(Γ) type spaces, and then conclude that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Banach, S.: Theoriě des opěrations Liněaires, Monografje Matematyczne, Warszawa, 1932

  2. Tingley, D.: Isometries of the unit sphere. Geometriae Dedicata, 22, 371–378 1987

    Article  MathSciNet  MATH  Google Scholar 

  3. Ding, G. G.: On the extension of isometries between unit spheres of E and C(Ω). Acta Mathematica Sinica, English Series, 19(4), 793–800 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ding, G. G.: The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space. Science in China, 45(4), 479–483 (2002)

    Article  MATH  Google Scholar 

  5. Mayer-Nieberg, P.: Banach Lattices, Springer-Verlag, Berlin-Heildelberg-New York, 1991

  6. Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces II, Springer-Verlag, Berlin-Heildelberg-New York, 1979

  7. Ma, Y. M.: Isometries of the unit spheres. Acta Math Sci, 12, 366–373 (1992)

    MATH  Google Scholar 

  8. Day, M. M.: Normed Linear Spaces, Springer-Verlag, Berlin-Heildelberg-New York, 1973

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guang Gui Ding.

Additional information

The project is supported by National Science Foundation of China (19971046) and the Doctoral Programme Foundation of Ministry of Education of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, G.G. The Representation Theorem of onto Isometric Mappings between Two Unit Spheres of l 1(Γ) Type Spaces and The Application to the Isometric Extension Problem. Acta Math Sinica 20, 1089–1094 (2004). https://doi.org/10.1007/s10114-004-0447-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-004-0447-7

Keywords

MR (2000) Subject Classification

Navigation