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The isometrical extensions of 1-Lipschitz mappings on Gâteaux differentiability spaces

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Abstract

Let X and Y be real Banach spaces. Suppose that the subset sm[S 1(X)] of the smooth points of the unit sphere S 1(X) is dense in S 1(X). If T 0 is a surjective 1-Lipschitz mapping between two unit spheres, then, under some condition, T 0 can be extended to a linear isometry on the whole space.

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Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, China

    GuangGui Ding

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  1. GuangGui Ding
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Correspondence to GuangGui Ding.

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Ding, G. The isometrical extensions of 1-Lipschitz mappings on Gâteaux differentiability spaces. Sci. China Math. 54, 711–722 (2011). https://doi.org/10.1007/s11425-010-4163-8

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