赋范空间E和l~1(Γ)的单位球面间等距映射的延拓

方习年;王建华;

数学学报 ›› 2008, Vol. 51 ›› Issue (1) : 23-28.

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数学学报 ›› 2008, Vol. 51 ›› Issue (1) : 23-28. DOI: 10.12386/A2008sxxb0003
论文

赋范空间E和l~1(Γ)的单位球面间等距映射的延拓

    方习年;王建华;
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Extension of Isometries Between Unit Spheres of Normed Space E and l~1(Γ)

    Xi Nian FANG(1); Jian Hua WANG
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摘要

研究赋范空间E和l~1(Γ)的单位球面之间的等距映射的延拓,得到E和l~1(Γ)的单位球面之间的满等距映射可以延拓为全空间E上的实线性等距算子,从而肯定地回答了相应的Tingley问题.

Abstract

We study the extension of isometries between the unit spheres of normed space E and l~1(F).We obtain that any surjective isometry between the unit spheres of normed space E and l~1(F)can be extended to be a linear isometry on the whole space E,and give an affirmative answer to the corresponding Tingley's problem.

关键词

等距映射 / Tingley问题 / 等距延拓

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方习年;王建华;. 赋范空间E和l~1(Γ)的单位球面间等距映射的延拓. 数学学报, 2008, 51(1): 23-28 https://doi.org/10.12386/A2008sxxb0003
Xi Nian FANG(1); Jian Hua WANG. Extension of Isometries Between Unit Spheres of Normed Space E and l~1(Γ). Acta Mathematica Sinica, Chinese Series, 2008, 51(1): 23-28 https://doi.org/10.12386/A2008sxxb0003
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