Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (3): 469-479.doi: 10.1016/S0252-9602(09)60047-3

• Articles • Previous Articles     Next Articles

THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE TO THE UNIT SPHERE S(E)

Ding Guanggui   

  1. School of Mathematical Sciemces and LPMC, Nankai University, Tianjin 300071, China
  • Received:2008-04-23 Online:2009-05-20 Published:2009-05-20
  • Supported by:

    This research was supported by the National Natural Science Foundation of China (10871101) and the Research Fund for the Doctoral Program of Higher Education (20060055010)

Abstract:

This is such a article to consider an ``into" isometric mapping between two unit spheres of two infinite dimensional spaces of different types. In this article, we find a useful condition (using the Krein-Milman property) under which an into-isometric mapping from the unit sphere of l(Γ) to the unit sphere of a normed space E can be linearly isometric extended.

Key words: isometric extension, extreme point, Krein-Milman property

CLC Number: 

  • 46A22
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