  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.

Functional Analysis