Corollary 2

If $(E_\alpha, f_{\beta \alpha})$ is a direct system of left $A$*-modules and* $E = \lim \longrightarrow E_\alpha$, $(E_\alpha^*, t f_{\beta \alpha})$ is an inverse system of right $A$*-modules and* $\lim \leftarrow E_\alpha^*$ is canonically isomorphic to $E^*$.