Skip to main content
SpringerLink
Log in

Extension of Isometries Between the Unit Spheres of Normed Space E and C (Ω)

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

Abstract

In this paper, we study the extension of isometries between the unit spheres of normed space E and C(Ω). We obtain that any surjective isometry between the unit spheres of normed space E and C(Ω) can be extended to be a linear isometry on the whole space E and give an affirmative answer to the corresponding Tingley’s problem (where Ω be a compact metric space).

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. Mazur, S., Ulam, S.: Sur less transformations isometriques d’espaces vectoriels normés. C. R. Acad. Paris., 194, 946–948 (1932)

    MATH  Google Scholar 

  2. Mankiewicz, P.: On extension of isometries in normed linear spaces. Bull. Acad. Polon, Sci. Ser. Sci. Math. Astronomy, Phys., 20, 367–371 (1972)

    MATH  MathSciNet  Google Scholar 

  3. Tingley, D.: Isometries of the unit sphere. Geometriae Dedicta, 22, 371–378 (1987)

    MATH  MathSciNet  Google Scholar 

  4. Ding, G. G.: The isometric extension problem in the unite spheres of l p(Γ)(p > 1) type spaces. Science in China, Ser. A, 32(11), 991–995 (2002)

    Google Scholar 

  5. Ding, G. G.: The representation theorem of onto isometric mappings between two unit spheres of l 1(Γ) type spaces and the application to isometric extension problem. Acta Math. Sinica, English Series, 20(6), 1089–1094 (2004)

    Article  MATH  Google Scholar 

  6. Ding, G. G.: On extensions and approximations of isometric operators (in Chinese). Advances in Mathematics, 32(5), 529–536 (2003)

    Google Scholar 

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

    Article  MATH  Google Scholar 

  8. Wang, R., Orihara, A.: Isometries on the l1-sum of C 0(Ω,E) type spaces. J. Math. Sci. Univ. Tokyo, 2, 131–154 (1995)

    MathSciNet  Google Scholar 

  9. Mahlon, M. Day.: Normed linear spaces, Springer-Verlag, Berlin, Heidelberg, New York, 1973

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Nanjing Audit University, Nanjing 210029, P. R. China

    Xi Nian Fang

  2. Department of Mathematics, Anhui Normal University, Wuhu 241000, P. R. China

    Jian Hua Wang

Authors
  1. Xi Nian Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Hua Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xi Nian Fang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fang, X.N., Wang, J.H. Extension of Isometries Between the Unit Spheres of Normed Space E and C (Ω). Acta Math Sinica 22, 1819–1824 (2006). https://doi.org/10.1007/s10114-005-0725-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-005-0725-z

Keywords

MR (2000) Subject Classification

Search

Navigation