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December 2012 Isometries and Maps Compatible with Inverted Jordan Triple Products on Groups
Osamu HATORI, Go HIRASAWA, Takeshi MIURA, Lajos MOLNÁR
Tokyo J. Math. 35(2): 385-410 (December 2012). DOI: 10.3836/tjm/1358951327

Abstract

Motivated by the famous Mazur-Ulam theorem in this paper we study algebraic properties of isometries between metric groups. We present some general results on so-called $d$-preserving maps between subsets of groups and apply them in several directions. We consider $d$-preserving maps on certain groups of continuous functions defined on compact Hausdorff spaces and describe the structure of isometries between groups of functions mapping into the circle group $\mathbb T$. Finally, we show a generalization of the Mazur-Ulam theorem for commutative groups and present a metric characterization of normed real-linear spaces among commutative metric groups.

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Osamu HATORI. Go HIRASAWA. Takeshi MIURA. Lajos MOLNÁR. "Isometries and Maps Compatible with Inverted Jordan Triple Products on Groups." Tokyo J. Math. 35 (2) 385 - 410, December 2012. https://doi.org/10.3836/tjm/1358951327

Information

Published: December 2012
First available in Project Euclid: 23 January 2013

zbMATH: 1271.46010
MathSciNet: MR3058715
Digital Object Identifier: 10.3836/tjm/1358951327

Subjects:
Primary: 46B04
Secondary: 46B28, 46J10, 47B49

Rights: Copyright © 2012 Publication Committee for the Tokyo Journal of Mathematics

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Vol.35 • No. 2 • December 2012
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