We study pairs $(U,L_0)$, where $U$ is a unitary operator in $H$ and $L_0\subset H$ is a closed subspace, such that $$ P_{L_0}U|_{L_0}:L_0\to L_0 $$ has a singular value decomposition. Abstract characterizations of this condition are given, as well as relations to the geometry of projections and pairs of projections. Several concrete examples are examined.

中文翻译：

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具有可分解角的酉算子

我们研究对 $(U,L_0)$，其中 $U$ 是 $H$ 中的酉算子，$L_0\subset H$ 是一个闭子空间，使得 $$ P_{L_0}U|_{L_0}： L_0\to L_0 $$ 有奇异值分解。给出了这种条件的抽象特征，以及与投影和投影对的几何关系。考察了几个具体的例子。