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Mathematical Physics, Analysis and Geometry

, Volume 13, Issue 4, pp 287–297 | Cite as

The Representation of Isometric Operators on C (1)(X)

  • Jingke LiEmail author
Article
  • 47 Downloads

Abstract

In this paper,we introduce a new norm on C (1)(X), which is induced by a hexagon on R 2, and prove that every isometric operator on C (1)(X) can be induced by a homeomorphism of X, where X is a connected subset of R.

Keywords

Hexagon Isometry Extreme point 

Mathematics Subject Classification (2010)

46B04 

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References

  1. 1.
    Wang, R.: Linear isometric operators on the C 0 (n)(X) type spaces. Kodai Math. J. 19, 259–281 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Pathak, V.D.: Isometrics of C n[0, 1]. Pac. J. Math. 94, 211–222 (1981)Google Scholar
  3. 3.
    De Leeuw, K.: Banach spaces of Lipschitz functions. Stud. Math. 21, 55–66 (1961)zbMATHGoogle Scholar
  4. 4.
    Jarosz, K., Pathak, V.D.: Isometries between function spaces. Trans. Am. Math. Soc. 305(1), 193–206 (1988)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.School of Mathematical SciencesNankai UniversityTianjinChina

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