华东师范大学学报(自然科学版) ›› 2006, Vol. 2006 ›› Issue (5): 8-12.

• 数学 统计学 • 上一篇    下一篇

非线性等距算子的特征

邓理进   

  1. 常州工学院 教育学院, 江苏 常州 213002
  • 收稿日期:2005-01-06 修回日期:2005-06-06 出版日期:2006-09-25 发布日期:2012-11-27

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

摘要： 讨论了无穷维Banach空间中非线形等距算子的特征. 在像空间是严格凸的要求下, 证明只要f:X-->Y,保持距离a,b,ma+nb, 其中a,b∈R+, m,n∈N,则f,一定是一个等距算子.这个结果在一定意义下回答了著名的Aleksandrov问题.

关键词: 等距算子, 严格凸, 保a算子 ,  ,

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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