Year: 2026
Type: preprint
Abstract: Let $\cH$ be a separable complex Hilbert space with $\dim\cH\ge3$. 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 $ψ$.
Source: arXiv (Cornell University)
Authors: Anzai, Mayu, Oi, Shiho
Institution: Niigata University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204233533