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Additive preservers of mutual strong numerical radius orthogonality
Abstract
Let H be a complex Hilbert space with dim H≥2. We show that the additive surjections on ℬ(H) and on its self-adjoint part ℬs(H) that preserve mutual strong numerical-radius orthogonality in one direction are precisely the maps of the form A↦ cUAU*, where U is a unitary or antiunitary operator on H and c is a nonzero complex or real scalar, respectively.
Related
- Orthograph related to mutual (strong) numerical radius orthogonality on operator algebra
- Spectral and numerical radius preservers on pairs of unitarily similar operators
- Orthogonality relation between GL(3) coefficients and additive characters with linear and non-linear phases
- On symmetricity of orthogonality with respect to numerical radius norm
- Strong convergence of Euler-Maruyama schemes for additive fractional SDEs with Lipschitz drift
BibTeX
@misc{tian2026additive,
title = {{Additive preservers of mutual strong numerical radius orthogonality}},
author = {Yulong Tian and Jinli Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39080},
eprint = {2610.39080},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39080},
}
RIS
TY - UNPB
TI - Additive preservers of mutual strong numerical radius orthogonality
AU - Yulong Tian
AU - Jinli Xu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39080
UR - https://arxiv.org/abs/2610.39080
AB - Let H be a complex Hilbert space with dim H≥2. We show that the additive surjections on ℬ(H) and on its self-adjoint part ℬ_s(H) that preserve mutual strong numerical-radius orthogonality in one direction are precisely the maps of the form A↦ cUAU^*, where U is a unitary or antiunitary operator on H and c is a nonzero complex or real scalar, respectively.
ER -