  We establish very general criteria for the existence of multiplication
operators between noncommutative Orlicz spaces $L^{\psi_0}(\tM)$ and
$L^{\psi_1}(\tM)$. We then show that these criteria contain existing results,
before going on to briefly look at the extent to which the theory of
multipliers on Orlicz spaces differs from that of $L^p$-spaces. In closing we
describe the compactness properties of such operators.
