b(2)空间及b(2)空间上的等距映射

王瑞东, 王普

数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 303-318.

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PDF(952 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 303-318. DOI: 10.12386/A2019sxxb0029
论文

b(2)空间及b(2)空间上的等距映射

    王瑞东, 王普
作者信息 +

b(2) Space and Isometries on b(2) Spaces

    Rui Dong WANG, Pu WANG
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文章历史 +

摘要

等距映射在空间结构的研究中起着很重要的作用,是泛函分析研究的有利工具. 本文将介绍一类特殊的F空间,b(2)空间, 然后给出该空间单位球面间满等距映射的表现定理,进而得出b(2)空间单位球面上满等距映射的线性延拓结论.

Abstract

Isometry is a significant subject in the study of the structure of space. In this paper, we will introduce a special F-space,b(2) space, and give the representation theorem for the onto isometric mapping on the unit spheres of the b(2) spaces, then we solved the Tingley's problem on b(2) space.

关键词

b(2)空间 / 闭球套 / 等距映射 / 线性延拓 / 表现定理

Key words

b(2) space / nested sequence of closed balls / isometry / linear extension / representation theorem

引用本文

导出引用
王瑞东, 王普. b(2)空间及b(2)空间上的等距映射. 数学学报, 2019, 62(2): 303-318 https://doi.org/10.12386/A2019sxxb0029
Rui Dong WANG, Pu WANG. b(2) Space and Isometries on b(2) Spaces. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 303-318 https://doi.org/10.12386/A2019sxxb0029

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基金

国家自然科学基金资助项目(NSFC11301384)

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