  A derivation $\delta$ on a $C^*$-algebra has kernel stabilization if for all
$n\in \mathbb{N}$, $\ker \delta^n=\ker \delta.$ Our main result shows that a
weakly-defined derivation studied recently by E. Christensen has kernel
stabilization. As corollaries, we (1) show that a family of $*$-derivations on
$C^*$-algebras studied by Bratteli and Robinson has kernel stabilization and
(2) provide sufficient conditions for when operators satisfying the Heisenberg
Commutation Relation must both be unbounded.
