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arXiv · 1911.03767

Any isometry between the spheres of absolutely smooth $2$-dimensional Banach spaces is linear

Taras Banakh
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Abstract

We prove that any isometry between the unit spheres of $C^2$-smooth (more generally, absolutely smooth) smooth Banach spaces extends to a linear isometry of the Banach spaces. This answers the famous Tingley's problem in the class of absolutely smooth $2$-dimensional Banach spaces.

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BibTeXRIS

Taras Banakh. 2019-11-09. Any isometry between the spheres of absolutely smooth $2$-dimensional Banach spaces is linear. https://doi.org/10.1016/j.jmaa.2021.125104

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