  Some new characterizations of nonnegative Hamiltonian operator matrices are
given. Several necessary and sufficient conditions for an unbounded nonnegative
Hamiltonian operators to be invertible are obtained; so that the main results
in the previously published papers are corollaries of the new theorems. Most of
all we want to stress the method of proof. It is based on the connections
between Pauli operator matrices and nonnegative Hamiltonian matrices.
