Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] S. V. Kislyakov, D. V. Maksimov, “Izomorfnyi tip prostranstva gladkikh funktsii, porozhdennogo konechnym semeistvom differentsialnykh operatorov”, Zap. nauchn. semin. POMI, 327, 2005, 78–97 | MR | Zbl

[2] C. C. Graham, O. C. McGehee, Essays in commutative harmonic analysis, Springer, Berlin, 1979 | MR