JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (2): 44-48.doi: 10.6040/j.issn.1671-9352.0.2016.225

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Linear extension of isometries between the unit spheres of two-dimensional normed spaces

LIU Xiao-wei   

  1. Department of Mathematics, School of Science, Tianjin University, Tianjing 300350, China
  • Received:2016-05-19 Online:2017-02-20 Published:2017-01-18

Abstract: We study the extension of isometries between the unit spheres S(E) and S(F), where E and F are both 2-dimensional real normed space. It is proved that surjective isometry V0 defined from S(E) to S(F) can be extended to be a linearly isometry V defined on the whole space S(E) under the some conditions.

Key words: Tingleys problem, isometry, linear extension

CLC Number: 

  • O177.2
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