非满等距映射的线性延拓

王瑞东;

数学学报 ›› 2006, Vol. 49 ›› Issue (6) : 1335-133.

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数学学报 ›› 2006, Vol. 49 ›› Issue (6) : 1335-133. DOI: 10.12386/A2006sxxb0168
论文

非满等距映射的线性延拓

    王瑞东;
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On Linear Extension of Isometries Between Unit Spheres

    Rui Dong WANG
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摘要

主要研究实赋范空间E和F的单位球面S_1(E)和S_1(F)之间的等距映射的线性延拓问题.得到:若等距映射V_0:S_1(E)→S_1(F)满足一定条件,则V_0可延拓为全空间E上的线性等距映射V:E→F,这是我们首次在非满的情况下考虑Tingley问题.

Abstract

we study the extension of isometries between the unit spheres S_1 (E) and S_1 (F),where E and F are both real normed spaces.We obtain that if the non-surjective isometry V_0 from S_1 (E) to S_1 (F) satisfy some properties,the V_0 can be extended to be real linearly isometric map V of E into F.This is the first time we study Tingley' problem without the condition of surjectivity.

关键词

线性延拓 / 等距 / Tingley问题

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王瑞东;. 非满等距映射的线性延拓. 数学学报, 2006, 49(6): 1335-133 https://doi.org/10.12386/A2006sxxb0168
Rui Dong WANG. On Linear Extension of Isometries Between Unit Spheres. Acta Mathematica Sinica, Chinese Series, 2006, 49(6): 1335-133 https://doi.org/10.12386/A2006sxxb0168
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