发表机构
Niigata University（新潟大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究可分复希尔伯特空间上有界线性算子代数的连续双射线性映射，刻画其保持C对称算子集合的条件，证明该条件等价于存在标准正交基集合的双射实现对角算子集合的映射。
AI 中文摘要
设H为可分复希尔伯特空间，本文研究H上所有有界线性算子构成的代数上的连续双射线性映射T。我们刻画了将所有C对称算子集合映射为所有ψ(C)对称算子集合的映射T，其中ψ是所有共轭算子集合上保交换性的双射。此外，我们证明该条件等价于存在H的所有标准正交基集合上的双射φ，使得T将所有{eₙ}对角算子集合映射为所有φ({eₙ})对角算子集合。
英文摘要
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 $ψ$.
