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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Acknowledgements
The authors express their deep gratitude to Professor Ding Guanggui for his encouragement and advice.
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Supported by National Natural Science Foundation of China (Grant Nos. 11301384, 11371201, 11201337 and 11201338)
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Wang, R.D., Huang, X.J. Isometries and additive mapping on the unit spheres of normed spaces. Acta. Math. Sin.-English Ser. 33, 1431–1442 (2017). https://doi.org/10.1007/s10114-017-6589-1
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DOI: https://doi.org/10.1007/s10114-017-6589-1