I'm trying to prove that $X$ is closed in $X''$, where $X$ is a Banach space. I know that $X$ is embeddable in $X''$.
If the isomorphism was bijective, I could show that $X$ is closed since $X''$ closed and closeness is preserved. But in general, it isn't bijective.
Which approach should I take? Hints only please, if possible.