I have a question. It is always true that if $E$ is an e.v.n, then $E''$ (Bidual) is Banach?. I've been looking at a proof that if $x_k$ converges weakly to 0 and is also Cauchy, then it converges strongly to 0. And it uses the isometry of canonical injection and that $E''$ is Banach to prove that it converges.
The answer in Spanish:
