Illinois Journal of Mathematics

Isometries between normed spaces which are surjective on a sphere

Ruidong Wang

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In this paper, we study the extension of isometric operator between unit spheres of normed spaces, and give an equivalent statement of Tingley problem. We also give another statement of Mazur–Ulam theorem: Let $V : E\rightarrow F$ be an isometric operator, and $V|_{S(E)}$ denotes the operator $V$ restricted to the set $S(E)$. If $V|_{S(E)}$ is an onto isometric operator from $S(E)$ to $S(F)$, then $V$ must be linear.

Article information

Illinois J. Math., Volume 53, Number 2 (2009), 575-580.

First available in Project Euclid: 23 February 2010

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Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces


Wang, Ruidong. Isometries between normed spaces which are surjective on a sphere. Illinois J. Math. 53 (2009), no. 2, 575--580. doi:10.1215/ijm/1266934793.

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