Nogawa, Tatsuya Uniqueness of the extension of isometries on the unit spheres in normed linear spaces. (English) Zbl 1323.46006 Nihonkai Math. J. 25, No. 2, 147-149 (2014). Summary: In this paper we show that the extension of a surjective isometry on the unit sphere in a normed linear space is unique. MSC: 46B04 Isometric theory of Banach spaces 46B20 Geometry and structure of normed linear spaces Keywords:Mazur-Ulam theorem; Tingley problem; isometry × Cite Format Result Cite Review PDF Full Text: Euclid References: [1] R. J. Fleming and J. E. Jamison, Isometries on Banach spaces: function spaces , Chapman Hall/CRC Monogr. Surv. Pure Appl. Math. 129 , Chapman & Hall/CRC, Boca Raton, 2003. · Zbl 1011.46001 [2] P. Mankiewicz, On extension of isometries in normed linear spaces , Bull. Acad. Polon. Sci. Sér. Sci. Math. Astron. Phys. 20 (1972), 367-371. · Zbl 0234.46019 [3] S. Mazur and S. Ulam, Sur les transformations isométriques d’espaces vectoriels normés , C. R. Acad. Sci. Paris 194 (1932), 946-948. · Zbl 0004.02103 [4] D. Tingley, Isometries of the unit sphere , Geom. Dedicata 22 (1987), 371-378. · Zbl 0615.51005 · doi:10.1007/BF00147942 [5] J. Väisälä, A proof of the Mazur-Ulam theorem , Amer. Math. Monthly 110 (2003), 633-635. · Zbl 1046.46017 · doi:10.2307/3647749 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.