A closed subspace of $\mathcal {D}(\Omega )$ which is not an $\mathrm {LF}$-space

With proper choice of region $\Omega \subseteq {R^n}$ and constant coefficient linear partial differential operator $P$, namely $\Omega$ being $P$-convex but not strong $P$-convex, the range of $P$ in $\mathcal {D}(\Omega )$ is a closed subspace of $\mathcal {D}(\Omega )$ whose subspace topology differs from its canonical ${\text {LF}}$-topology. In the present paper this result is proved and an example of a pair $\Omega ,\;P$ satisfying the above hypotheses is presented.