I'm trying to understand the definition of reflexive spaces. I wrote in my notes:
If $Y$ is reflexive then for all $\eta\in Y^{**}$, $f\in Y^*$, $\exists y\in Y$ where $\eta(f) = f(y)$.
My question is, is this for all $f$ or there exist some $f$? Wikipedia and Wolfram mathworld are not specific about it.
In Hilbert space it seems like for all $f$, but I have difficulty imagining other spaces.
Thanks!