Consider the following Theorem:
A $C^*$-algebra is $*$-isomorphic to a von Neumann algebra iff it is the dual of a Banach space.
The direction "von Neumann algebras have preduals" is clear to me, however I cannot find a proper reference for the other direction. In the book by Bratteli and Robinson it is remarked that this is proven in Theorem 1.16.7. in Sakai's paper On the central decomposition for positive functionals on *-algebras. However this Theorem doesn't exist in the paper and the paper is about something completely different, so I think they intended to reference another paper.
Where can one find a proof of the other direction?
Best Answer
The proof for the direction which you are looking for can be found as the proof of Theorem 1.16.7 in Sakai's book $C^*$-Algebras and $W^\ast$-Algebras.