Acta mathematica scientia, Series B >
THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE TO THE UNIT SPHERE S(E)
Received date: 2008-04-23
Online 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)
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
Ding Guanggui . THE ISOMETRIC EXTENSION OF AN INTO MAPPING FROM THE UNIT SPHERE TO THE UNIT SPHERE S(E)[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 469 -479 . DOI: 10.1016/S0252-9602(09)60047-3
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