I am trying to understand the predual space $X$ of $H_0^1(\Omega)$. My idea was to identify the predual space by the canonical embedding $i:X\to (H_0^1(\Omega))^{*}$. I know that a Hilbert space is isomorphic to its bidual space. I would like to say that $X$ is isomorphic to the dual space of $H_0^1(\Omega)$. But I think apriori this is not possible since I don't know if $X$ is reflexive. Am I mistaking, is it also possible to go backwards, so may I say that if $X''$ is a Hilbert space also $H$ is a Hilbert space ? My second thought was to use the theorem of Riesz-Frechet to identify $X$ with $H_0^1(\Omega)$. Unluckily I would also need that $X$ is a Hilbert space. I think I'm overlooking something.
Can anyone please help me gain a better understanding of what is going on here?