On isometric extensions and distance one preserving mappings

被引:8
作者
Ding, GG [1 ]
机构
[1] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China
来源
TAIWANESE JOURNAL OF MATHEMATICS | 2006年 / 10卷 / 01期
关键词
isometric extension; distance one preserving mapping;
D O I
10.11650/twjm/1500403815
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this survey article, we introduce the isometric extension problem of isometric mapping between the unit spheres and the distance one preserving problem. Some important results in the development of the related problems are outlined in this paper and some recent advancement and open problems are repointed.
引用
收藏
页码:243 / 249
页数:7
相关论文
共 37 条
[1]  
ALEKSANDROV A. D., 1970, SOV MATH DOKL, V11, P116
[2]   Isometries on unit sphere of (lβn) [J].
An, GM .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 301 (01) :249-254
[3]  
BANACH S, 1932, LINEAIRES THEORIE OP
[4]   ON ISOMETRIES OF EUCLIDEAN SPACES [J].
BECKMAN, FS ;
QUARLES, DA .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (05) :810-815
[5]  
BENZ W, 1985, AEQUATIONES MATH, V29, P204
[6]   On the Aleksandrov problem in linear n-normed spaces [J].
Chu, HY ;
Lee, KH ;
Park, CG .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 59 (07) :1001-1011
[7]   The Aleksandrov problem in linear 2-normed spaces [J].
Chu, HY ;
Park, CG ;
Park, WG .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 289 (02) :666-672
[8]  
DING G, IN PRESS ILLINOIS J
[9]   The representation theorem of onto isometric mappings between two unit spheres of l∞-type spaces and the application on isometric extension problem [J].
Ding, GG .
SCIENCE IN CHINA SERIES A-MATHEMATICS, 2004, 47 (05) :722-729
[10]   On the extension of isometries between unit spheres of E and C(Ω) [J].
Ding, GG .
ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2003, 19 (04) :793-800