Additive mappings preserving orthogonality between complex inner product spaces Li, Lei Liu, Siyu Peralta Pereira, Antonio Miguel Birkhoff orthogonality Euclidean orthogonality Orthogonality preserving additive mappings Inner product spaces L. Li was supported by National Natural Science Foundation of China (Grant No. 12171251). A.M. Peralta supported by grant PID2021-122126NB-C31 funded by MICIU/AEI/10.13039/501100011033 and by ERDF/EU, by Junta de Andalucía grant FQM375, IMAG–María de Maeztu grant CEX2020-001105-M/AEI/10.13039/ 501100011033 and (MOST) Ministry of Science and Technology of China grant G2023125007L. Let H and K be two complex inner product spaces with dim(H) ≥ 2. We prove that for each non-zero mapping A : H → K with dense image the following statements are equivalent: (a) A is (complex) linear or conjugate-linear mapping and there exists γ > 0 such that ‖A(x)‖ = γ‖x‖, for all x ∈ H, that is, A is a positive scalar multiple of a linear or a conjugate-linear isometry; (b) There exists γ1 > 0 such that one of the next properties holds for all x, y ∈ H: (b.1) 〈A(x)|A(y)〉 = γ1〈x|y〉, (b.2) 〈A(x)|A(y)〉 = γ1〈y|x〉; (c) A is linear or conjugate-linear and preserves orthogonal- ity; (d) A is additive and preserves orthogonality in both direc- tions; (e) A is additive and preserves orthogonality. 2025-04-03T12:37:06Z 2025-04-03T12:37:06Z 2025-03-01 journal article L. Li et al. Linear Algebra and its Applications 710 (2025) 448–457. https://doi.org/10.1016/j.laa.2025.01.042 https://hdl.handle.net/10481/103432 10.1016/j.laa.2025.01.042 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Elsevier