Stage G: normal von Neumann channels

For example, the algebra of compact operators plus scalars on an infinite-dimensional Hilbert space is ultraweakly dense in $\mathcal{B}(\mathcal{H})$. Two normal states agreeing there agree everywhere, so normal-state determinacy cannot detect membership in that proper norm-closed subalgebra.

No normal conditional expectation has been added to Theorem thm:normal. Its optional state-preserving existence continues to require a separate criterion, as discussed in Section sec:expectations.