数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 161-165.doi: 10.1016/S0252-9602(10)60032-X

• 论文 • 上一篇    下一篇

ON LINEAR EXTENSION OF 1-LIPSCHITZ MAPPING FROM HILBERT SPACE INTO A NORMED SPACE

王瑞东   

  1. Department of Mathematics, Tianjin University of Technology, Tianjin 300191, China
  • 收稿日期:2007-03-01 修回日期:2007-12-20 出版日期:2010-01-20 发布日期:2010-01-20
  • 基金资助:

    Supported by  NSFC (10871101) and the Doctoral Programme Foundation of Institution of Higher Education
    (20060055010).

ON LINEAR EXTENSION OF 1-LIPSCHITZ MAPPING FROM HILBERT SPACE INTO A NORMED SPACE

 WANG Rui-Dong   

  1. Department of Mathematics, Tianjin University of Technology, Tianjin 300191, China
  • Received:2007-03-01 Revised:2007-12-20 Online:2010-01-20 Published:2010-01-20
  • Supported by:

    Supported by  NSFC (10871101) and the Doctoral Programme Foundation of Institution of Higher Education
    (20060055010).

摘要:

In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole
space.

关键词: Isometric extension, Tingley problem, Hilbert space

Abstract:

In this article, we prove that an into 1-Lipschitz mapping from the unit sphere of a Hilbert space to the unit sphere of an arbitrary normed space, which under some conditions, can be extended to be a linear isometry on the whole
space.

Key words: Isometric extension, Tingley problem, Hilbert space

中图分类号: 

  • 46B20