Tokyo Journal of Mathematics

Isometries and Maps Compatible with Inverted Jordan Triple Products on Groups

Osamu HATORI, Go HIRASAWA, Takeshi MIURA, and Lajos MOLNÁR

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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.

Article information

Source
Tokyo J. Math., Volume 35, Number 2 (2012), 385-410.

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1358951327

Digital Object Identifier
doi:10.3836/tjm/1358951327

Mathematical Reviews number (MathSciNet)
MR3058715

Zentralblatt MATH identifier
1271.46010

Subjects
Primary: 46B04: Isometric theory of Banach spaces
Secondary: 46B28: Spaces of operators; tensor products; approximation properties [See also 46A32, 46M05, 47L05, 47L20] 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 47B49: Transformers, preservers (operators on spaces of operators)

Citation

HATORI, Osamu; HIRASAWA, Go; MIURA, Takeshi; MOLNÁR, Lajos. Isometries and Maps Compatible with Inverted Jordan Triple Products on Groups. Tokyo J. Math. 35 (2012), no. 2, 385--410. doi:10.3836/tjm/1358951327. https://projecteuclid.org/euclid.tjm/1358951327


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