论文标题
Wigner型定理的几何方法
A geometric approach to Wigner-type theorems
论文作者
论文摘要
令$ h $为复杂的希尔伯特空间，让$ {\ Mathcal p}（h）$为相关的投影空间（一组排名一的预测）。假设$ \ dim H \ ge 3 $。我们证明了以下Wigner-type定理：如果$ h $是有限的，那么$ {\ Mathcal p}（h）$的每个正交性保留转换都是由单一或反独立的操作员诱导的。该语句将是由于以下结果而获得的：每种正交性保留$ {\ Mathcal p}（h）$本身的lineation均由线性或结合线性等轴测图引起（假定$ h $不假定为有限的二级）。作为一种应用，我们描述了（不一定是抹香间）的拉格曼人的转变，以保留某些类型的主要角度。
Let $H$ be a complex Hilbert space and let ${\mathcal P}(H)$ be the associated projective space (the set of rank-one projections). Suppose that $\dim H\ge 3$. We prove the following Wigner-type theorem: if $H$ is finite-dimensional, then every orthogonality preserving transformation of ${\mathcal P}(H)$ is induced by a unitary or anti-unitary operator. This statement will be obtained as a consequence of the following result: every orthogonality preserving lineation of ${\mathcal P}(H)$ to itself is induced by a linear or conjugate-linear isometry ($H$ is not assumed to be finite-dimensional). As an application, we describe (not necessarily injective) transformations of Grassmannians preserving some types of principal angles.
