Predual of a von Neumann algebra

Question

Let $M$ be a von Neumann algebra. Can we view the predual $M_{*}$ of $M$ as a closed subspace of $M^*$?

Answer 1

Your question is not really about von Neumann algebras, but rather about Banach spaces admitting a predual (which the class of von Neumann algebras satisfies).

The predual $M_*$ is a Banach space such that $(M_*)^* \cong M$. Thus we have $$M_* \subseteq (M_*)^{**} \cong M^*$$

The inclusion $M_* \subseteq (M_*)^{**}$ via the canonical map $v \mapsto \operatorname{ev}_v$ is isometric and $M_*$ is a Banach space, so the answer to your question is yes.