  An operator Riccati equation from systems theory is considered in the case
that all entries of the associated Hamiltonian are unbounded. Using a certain
dichotomy property of the Hamiltonian and its symmetry with respect to two
different indefinite inner products, we prove the existence of nonnegative and
nonpositive solutions of the Riccati equation. Moreover, conditions for the
boundedness and uniqueness of these solutions are established.
