Acta mathematica scientia,Series B ›› 2010, Vol. 30 ›› Issue (1): 161-165.doi: 10.1016/S0252-9602(10)60032-X

• Articles • Previous Articles     Next Articles

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).

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

CLC Number: 

  • 46B20
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