Remark: Not operator-norm convergence

The convergence is state-relative and spectral. It is not operator-norm convergence of unbounded fields, and it is not uniform over all states. Even for the bounded Weyl functions, if $v\ne 0$, the spectrum of $\Phi (v)$ is $\mathbb{R}$, and

The theorem therefore makes no norm-continuous identification of the entire quantum algebra with a classical algebra.