@misc{10481/103432,
year = {2025},
month = {3},
url = {https://hdl.handle.net/10481/103432},
abstract = {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.},
organization = {National Natural Science Foundation of China (12171251)},
organization = {MICIU/AEI/10.13039/501100011033 PID2021-122126NB-C31},
organization = {ERDF/EU},
organization = {Junta de Andalucía  FQM375},
organization = {IMAG–María de Maeztu grant CEX2020-001105-M/AEI/10.13039/ 501100011033},
organization = {(MOST) Ministry of Science and Technology of China  G2023125007L},
publisher = {Elsevier},
keywords = {Birkhoff orthogonality},
keywords = {Euclidean orthogonality},
keywords = {Orthogonality preserving additive mappings},
keywords = {Inner product spaces},
title = {Additive mappings preserving orthogonality between complex inner product spaces},
doi = {10.1016/j.laa.2025.01.042},
author = {Li, Lei and Liu, Siyu and Peralta Pereira, Antonio Miguel},
}