论文标题
紧凑的自动化操作员的共轭类别的转换，保留转换
Commutativity preserving transformations on conjugacy classes of compact self-adjoint operators
论文作者
论文摘要
令$ h $成为一个复杂的希尔伯特尺寸空间，不少于$ 3 $，让$ {\ Mathcal C} $是$ h $上的紧凑型自我接合运算符的共轭类。假设运算符的内核与$ {\ Mathcal C} $的尺寸不小于其范围的尺寸。如果$ {\ Mathcal C} $由有限等级$ K $和$ \ dim H = 2K $的运营商形成时，我们假设$ k \ ge 4 $。我们表明，C保留两个方向上的通勤性的每种b。单位或反独立的操作员都会诱发同一维度特征空间的排列。
Let $H$ be a complex Hilbert space of dimension not less than $3$ and let ${\mathcal C}$ be a conjugacy class of compact self-adjoint operators on $H$. Suppose that the dimension of the kernels of operators from ${\mathcal C}$ not less than the dimension of their ranges. In the case when ${\mathcal C}$ is formed by operators of finite rank $k$ and $\dim H=2k$, we assume that $k\ge 4$. We show that every bijective transformation of C preserving the commutativity in both directions is induced by a unitary or anti-unitary operator up to a permutation of eigenspaces of the same dimension.
