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The 1-Lipschitz mapping between the unit spheres of two Hilbert spaces can be extended to a real linear isometry of the whole space
Authors:Guanggui Ding
Institution:Department of Mathematics, Nankai University, Tianjin 300071, China
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.
Keywords:isometric mapping  strictly convex  smooth point
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