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期刊论文
The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space
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Let E and F be Hilbert spaces with unit spheres S1(E) and S1(F). Suppose that V0 S1(E)→S1(F) is a Lipschitz mapping with lipschitz constantk=1Such that-V0[S1(E)]++V0[S1(E)], then V0 can be extended to a real linear isometric mapping V from E into F. In particular, every isometric mapping from S1(E) onto S (F) can be extended to a real linear isometric mapping from E onto F.
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