数学物理学报(英文版)

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ISOMETRIES ON THE SPACE s

傅小红   

  1. 南开大学数学系, 天津 300071
  • 收稿日期:2004-09-08 修回日期:1900-01-01 出版日期:2006-07-20 发布日期:2006-07-20
  • 通讯作者: 傅小红
  • 基金资助:

    Supported by the National Science Foundation of China (10571090) and The Research Fund for the Doctoral Program of Higher Education (20010055013).

ISOMETRIES ON THE SPACE s

Fu Xiaohong   

  1. Department of Mathematics, Nankai University, Tianjin 300071, China
  • Received:2004-09-08 Revised:1900-01-01 Online:2006-07-20 Published:2006-07-20
  • Contact: Fu Xiaohong

摘要:

In this article, the author presents some results of the isometric linear extension from some spheres in the finite dimensional space s(n). Moreover, the author presents the representation for the onto isometric mappings in the space s. It is obtained that if V is a surjective isometry from the space s onto s with V(0)={0}, then V must be real linear.

关键词: Isometric mapping, isometric extension, Mazur-Ulam theorem, representation

Abstract:

In this article, the author presents some results of the isometric linear extension from some spheres in the finite dimensional space s(n). Moreover, the author presents the representation for the onto isometric mappings in the space s. It is obtained that if V is a surjective isometry from the space s onto s with V(0)={0}, then V must be real linear.

Key words: Isometric mapping, isometric extension, Mazur-Ulam theorem, representation

中图分类号: 

  • 46B04