  We provide a direct, intersection theoretic, argument that the Jordan models
of an operator of class C_{0}, of its restriction to an invariant subspace, and
of its compression to the orthogonal complement, satisfy a multiplicative form
of the Horn inequalities, where `inequality' is replaced by `divisibility'.
When one of these inequalities is saturated, we show that there exists a
splitting of the operator into quasidirect summands which induces similar
splittings for the restriction of the operator to the given invariant subspace
and its compression to the orthogonal complement. The result is true even for
operators acting on nonseparable Hilbert spaces. For such operators the usual
Horn inequalities are supplemented so as to apply to all the Jordan blocks in
the model.
