Please use this identifier to cite or link to this item:
http://hdl.handle.net/10662/19970
Title: | A reflection on Tingley's problem and some applications |
Authors: | Cabello Sánchez, Javier |
Keywords: | Propiedad de Mazur-Ulam;Mazur-Ulam property;Invariantes métricos;metric invariants;espacios estrictamente convexos;strictly convex spaces;curvatura;curvature |
Issue Date: | 2019 |
Publisher: | Elsevier |
Abstract: | In this paper we show how some metric properties of the unit sphere of a normed space can help to approach a solution to Tingley’s problem. In our main result we show that if an onto isometry between the spheres of strictly convex spaces is the identity when restricted to some relative open subset, then it is the identity. This implies that an onto isometry between the unit spheres of strictly convex finite dimensional spaces is linear if and only it is linear on a relative open set. We prove the same for arbitrary two-dimensional spaces and obtain that every two-dimensional, non strictly convex, normed space has the Mazur-Ulam Property. |
URI: | http://hdl.handle.net/10662/19970 |
DOI: | 10.1016/j.jmaa.2019.03.041 |
Appears in Collections: | DMATE - Artículos |
Files in This Item:
File | Description | Size | Format | |
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2019Reflection.pdf | 472,73 kB | Adobe PDF | View/Open |
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