Acta Mathematica Sinica

, Volume 22, Issue 6, pp 1819–1824

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

ORIGINAL ARTICLES

DOI: 10.1007/s10114-005-0725-z

Cite this article as:
Fang, X.N. & Wang, J.H. Acta Math Sinica (2006) 22: 1819. doi:10.1007/s10114-005-0725-z

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).

Keywords

isometric mapping isometric extension Tingley’s problem 

MR (2000) Subject Classification

46B04 46B20 47A67 51K05 

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Department of Applied MathematicsNanjing Audit UniversityNanjing 210029P. R. China
  2. 2.Department of MathematicsAnhui Normal UniversityWuhu 241000P. R. China

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