论文标题
在Birman-Krein定理上
On the Birman-Krein Theorem
论文作者
论文摘要
结果表明，如果$ x $是统一运算符，那么〜$ u $的单数子空间在单位上等同于〜$ ux $（或$ xu $）的单数子空间，而对于每个单位运算符〜$ u $，那么$ x $是身份操作员。换句话说，Birman-Krein定理没有非平凡的概括，其中包括在这种情况下保存单数光谱子空间。
It is shown that if $X$ is a unitary operator so that a singular subspace of~$U$ is unitarily equivalent to a singular subspace of~$UX$ (or $XU$), for each unitary operator~$U$, then $X$ is the identity operator. In other words, there is no nontrivial generalization of Birman-Krein Theorem that includes the preservation of a singular spectral subspace in this context.
