  In this supplement to [GJ1], [GJ3], we give an intrinsic characterization of
(bounded, linear) operators on Banach lattices which factor through Banach
lattices not containing a copy of $c_0$ which complements the characterization
of [GJ1], [GJ3] that an operator admits such a factorization if and only if it
can be written as the product of two operators neither of which preserves a
copy of $c_0$. The intrinsic characterization is that the restriction of the
second adjoint of the operator to the ideal generated by the lattice in its
bidual does not preserve a copy of $c_0$. This property of an operator was
introduced by C. Niculescu [N2] under the name ``strong type B".
