PreprintCC BY 4.0arXiv
Linear maps preserving families of C-symmetric operators
Abstract
Let cH be a separable complex Hilbert space with dimcH≥3. We characterize the bounded bijective complex-linear maps T on BH for which there exists a bijection ψ of the set of conjugations,preserving commutativity in both directions, such that T maps the space of C-symmetric operators onto the space of ψ(C)-symmetric operators for every conjugation C. We show that this condition is equivalent to the existence of a bijection φ of the set of all orthonormal bases such that T maps the set of all (en)-diagonal operators onto the set of all φ((en))-diagonal operators. We also characterize the corresponding preservers in dimension two using Pauli coordinates, without assuming the commutativity condition on ψ.
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BibTeX
@misc{anzai2026linear,
title = {{Linear maps preserving families of C-symmetric operators}},
author = {Mayu Anzai and Shiho Oi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.24583},
eprint = {2608.24583},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.24583},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Linear maps preserving families of C-symmetric operators
AU - Mayu Anzai
AU - Shiho Oi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2608.24583
UR - https://arxiv.org/abs/2608.24583
AB - Let cH be a separable complex Hilbert space with dimcH≥3. We characterize the bounded bijective complex-linear maps T on BH for which there exists a bijection ψ of the set of conjugations,preserving commutativity in both directions, such that T maps the space of C-symmetric operators onto the space of ψ(C)-symmetric operators for every conjugation C. We show that this condition is equivalent to the existence of a bijection φ of the set of all orthonormal bases such that T maps the set of all (e_n)-diagonal operators onto the set of all φ((e_n))-diagonal operators. We also characterize the corresponding preservers in dimension two using Pauli coordinates, without assuming the commutativity condition on ψ.
ER -