there's a question that I've be puzzling over for a little while now and I haven't made much progress, so I thought I'd better ask for some help. It is as follows:
Suppose that $\langle E,F\rangle$ are a pair of dual spaces. Prove that $E$ is $\sigma(E,F)$-complete iff $F$ is isomorphic to $E^*$.
I've managed to prove that $F$ isomorphic to $E^*$ implies that $E$ is $\sigma(E,F)$-complete, but I can seem to do it the other way around. Any suggestions?