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We prove that only inner product spaces allow nonzero mappings reversing Birkhoff orthogonality, suggesting a unique structural property.
In this article, we prove that among normed spaces of dimension greater than two, only inner product spaces admit nonzero additive mapping which reverse the Birkhoff orthogonality. In fact, such a mapping must be a linear similarity.
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Khurana et al. (2026) studied this question.
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