Illinois Journal of Mathematics

Isometries between normed spaces which are surjective on a sphere

Ruidong Wang

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Abstract

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

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

Dates
First available in Project Euclid: 23 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1266934793

Digital Object Identifier
doi:10.1215/ijm/1266934793

Mathematical Reviews number (MathSciNet)
MR2594644

Zentralblatt MATH identifier
1200.46018

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

Citation

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. https://projecteuclid.org/euclid.ijm/1266934793


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References

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