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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Authors: | Guanggui Ding |
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Institution: | Department of Mathematics, Nankai University, Tianjin 300071, China |
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Abstract: | LetE andF be Hilbert spaces with unit spheresS
1(E) andS
1(F). Suppose thatV
0 S1(E) →S
1(F) is a Lipschitz mapping with Lipschitz constantk=1 such that −V
0S
1(E)] ⊂V
0S
1(E)]. Then V0 can be extended to a real linear isometric mappingV fromE intoF. In particular, every isometric mapping fromS
1(E) ontoS
1(F) can be extended to a real linear isometric mapping fromE ontoF. |
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Keywords: | isometric mapping strictly convex smooth point |
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