论文标题
在二维圆环的平滑功能空间中，没有局部无条件结构
Absence of local unconditional structure in spaces of smooth functions on two-dimensional torus
论文作者
论文摘要
考虑一个有限的集合$ \ {t_1，\ ldots，t_j \} $的差分运算符，具有$ \ mathbb {t}^2 $的恒定系数以及该集合产生的平滑函数的空间，即功能$ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ f $ t_j f \ in c（c（\ m mathbb bbbbbbbb）我们证明，在某种自然条件下，这个空间与$ c（s）$ - 空间的商不同构，并且没有局部无条件结构。这一事实概括了先前已知的结果，即这种空间与$ c（s）$的补充子空间不是同构。
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 $T_j f \in C(\mathbb{T}^2)$. We prove 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 $C(S)$.
