  The C*-algebra of bounded operators on the separable infinite-dimensional
Hilbert space cannot be mapped to a W*-algebra in such a way that each unital
commutative C*-subalgebra C(X) factors normally through $\ell^\infty(X)$.
Consequently, there is no faithful functor discretizing C*-algebras to
AW*-algebras, including von Neumann algebras, in this way.
