Journal of East China Normal University(Natural Sc ›› 2006, Vol. 2006 ›› Issue (5): 8-12.

• Article • Previous Articles     Next Articles

Characterization of Non-Linear Isometries

DENG Li-jin   

  1. School of Education, Changzhou Institute of Technology, Changzhou Jiangsu
  • Received:2005-01-06 Revised:2005-06-06 Online:2006-09-25 Published:2012-11-27

Abstract: This paper studied the characterization of non-linear isometries between infinite dimensional Banach spaces.Under the assumption that the range space is strictly convex, it was proved that f:X-->Y is an isometry <==> it preserves the distance a,b,ma+nb for a,b∈R+, m,n∈N. Thus in some sense the Aleksandrov
problem was solved.

Key words: isometries, strictly convex, distance a preserving map

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