Abstract
Any orthogonally additive injection of a real inner product space of dimension at least 2 onto an abelian group is additive.
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References
Baron K.: On some orthogonally additive functions on inner product spaces. Ann. Univ. Budapest. Sect. Comput. 40, 123–127 (2013)
Baron K., Rätz J.: On orthogonally additive mappings on inner product spaces. Bull. Polish Acad. Sci. Math. 43, 187–189 (1995)
Rätz J.: On orthogonally additive mappings. Aequationes Math. 28, 35–49 (1985)
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Baron, K. Orthogonally additive bijections are additive. Aequat. Math. 89, 297–299 (2015). https://doi.org/10.1007/s00010-013-0242-6
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DOI: https://doi.org/10.1007/s00010-013-0242-6