二维赋范空间单位球面间的等距映射的线性延拓

doi:10.6040/j.issn.1671-9352.0.2016.225

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (2): 44-48.doi: 10.6040/j.issn.1671-9352.0.2016.225

二维赋范空间单位球面间的等距映射的线性延拓

刘晓伟

天津大学理学院数学系, 天津 300350

收稿日期:2016-05-19 出版日期:2017-02-20 发布日期:2017-01-18
作者简介:刘晓伟(1987— ),男,硕士研究生,研究方向为等距线性延拓相关问题. E-mail:wbswlgydjlxw@163.com

Linear extension of isometries between the unit spheres of two-dimensional normed spaces

LIU Xiao-wei

Department of Mathematics, School of Science, Tianjin University, Tianjing 300350, China

Received:2016-05-19 Online:2017-02-20 Published:2017-01-18

摘要/Abstract

摘要： 研究二维实赋范空间E和F的单位球面S(E)和S(F)之间的等距线性延拓问题,证明了在一定条件下,定义在单位球面S(E)和S(F)之间的满等距算子V0可延拓为全空间E上的等距线性算子V。

关键词: Tingley问题, 线性延拓, 等距

Abstract: We study the extension of isometries between the unit spheres S(E) and S(F), where E and F are both 2-dimensional real normed space. It is proved that surjective isometry V₀ defined from S(E) to S(F) can be extended to be a linearly isometry V defined on the whole space S(E) under the some conditions.

Key words: Tingleys problem, isometry, linear extension

中图分类号:

O177.2

刘晓伟. 二维赋范空间单位球面间的等距映射的线性延拓[J]. 山东大学学报（理学版）, 2017, 52(2): 44-48.

LIU Xiao-wei. Linear extension of isometries between the unit spheres of two-dimensional normed spaces[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 44-48.

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二维赋范空间单位球面间的等距映射的线性延拓

Linear extension of isometries between the unit spheres of two-dimensional normed spaces

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