  Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators
with constant coefficients on $\mathbb{T}^n$ ($n\geq 2$) and the space of
smooth functions generated by this collection, namely, the space of functions
$f$ such that $T_j f \in C(\mathbb{T}^n)$, $1\leq j\leq J$. We prove that if
there are at least two linearly independent operators among their senior parts
(relative to some mixed pattern of homogeneity), then this space does not have
local unconditional structure. This fact generalizes the previously known
result that such spaces are not isomorphic to a complemented subspace of $C(S)$
