If I have to normed vector spaces $A$ and $B$, I was wondering when the topological duals are isomorphic (i.e. $A^* \cong B^*)$ . Is it sufficient that $A \cong B$? Or that $A$ has to be isometric to $B$?
If it is sufficient for $A$ isometric to $B$, given an isometry $f$, what would be the isomorphism mapping between the spaces $A^*$ and $B^*$?