Abstract. 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.

DOI: 10.14232/actasm-015-538-z

AMS Subject Classification (1991): 47A15

Keyword(s): invariant subspaces, Horn inequalities

Received May 19, 2015. (Registered under 38/2015.)