Characterization of Non-Linear Isometries
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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,bR+, m,nN,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.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,bR+, m,nN. Thus in some sense the Aleksandrov problem was solved.
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Key words:
- isometries /
- strictly convex /
- distance a preserving map
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