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

A closed subspace of 𝒟(Ω) which is not an ℒℱ-space