Isomorphic type of the space of smooth functions determined by a finite family of differential operators

On the torus $\mathbb T^n$ with $n\ge 2$, the space mentioned in the title is not isomorphic to a complemented subspace of $C(K)$ if the finite family in question consists of homogeneous differential operators of one and the same order with constant coefficients and at least two among them are linearly independent.