Isometries and additive mapping on the unit spheres of normed spaces |
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Authors: | Rui Dong Wang Xu Jian Huang |
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Institution: | Science of College, Tianjin University of Technology, Tianjin 300384, P. R. China |
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Abstract: | In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres. |
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Keywords: | Isometric extension additive mapping unit sphere angle |
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