We can identify spaces $V$ and $V^{\*\*}$ by canonical isomorphism:
$$A:V\to V^{\*\*},$$
$$Av(f)=f(v),$$
for any $f\in V^\*$.

But why we cannot identify $V$ and $V^\*$ by $e^{\*}\_{i}(e\_j)=\delta\_{ij}$
(I understand that after change the basis of $V$ operator $B: V\to V^\*$ will be changed)?
What means that spaces $V$ and $V^{\*\*}$ are identical? How we can use it?