Geodesic
Absence of local unconditional structure in spaces of smooth functions on the two-dimensional torus
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 153-172

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Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^2$ and the space of smooth functions generated by this collection, namely, the space of functions $f$ such that $T_j f \in C(\mathbb{T}^2)$. It is proved that under a certain natural condition this space is not isomorphic to a quotient of a $C(S)$-space and does not have a local unconditional structure. This fact generalizes the previously known result that such spaces are not isomorphic to a complemented subspace of $C(S)$. 
@article{ZNSL_2020_491_a8,
     author = {A. Tselishchev},
     title = {Absence of local unconditional structure in spaces of smooth functions on the two-dimensional torus},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {153--172},
     publisher = {mathdoc},
     volume = {491},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a8/}
}
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A. Tselishchev. Absence of local unconditional structure in spaces of smooth functions on the two-dimensional torus. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 48, Tome 491 (2020), pp. 153-172. http://geodesic.mathdoc.fr/item/ZNSL_2020_491_a8/