In linear algebra, I’ve just shown that $V\cong V’’$, ie $V$ is isomorphic to its double dual.
I now want to show that if $U$ is a subspace of $V$ then $U$ is mapped isomorphically to $U^{00}$, ie the annihilator of the annihilator of $U$.
If $T:V\to V’’$ is the natural isomorphism, how can I show that $U\cong T(U)$?
Because I know $T(U)\subseteq U^{00}$, so I will be done.