Isomorphic type of the space of smooth functions determined by a~finite family of differential operators.~II
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 34, Tome 333 (2006), pp. 62-65

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The space of smooth function on $\mathbb T^3$ generated by one differential expression may fail to be isomorphic to a complemented subspace of $C(K)$. For instance, this happens for the differential expression $\partial^2_1-\partial^2_2-\partial^2_3$.
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     author = {D. V. Maksimov},
     title = {Isomorphic type of the space of smooth functions determined by a~finite family of differential {operators.~II}},
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D. V. Maksimov. Isomorphic type of the space of smooth functions determined by a~finite family of differential operators.~II. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 34, Tome 333 (2006), pp. 62-65. http://geodesic.mathdoc.fr/item/ZNSL_2006_333_a5/