Absence of local unconditional structure in spaces of smooth functions on the torus of arbitrary dimension

IF 0.7 3区 数学 Q2 MATHEMATICS Studia Mathematica Pub Date : 2021-04-07 DOI:10.4064/sm200629-21-12
A. Tselishchev
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引用次数: 0

Abstract

Consider a finite collection {T1, . . . , TJ} of differential operators with constant coefficients on Tn (n ≥ 2) and the space of smooth functions generated by this collection, namely, the space of functions f such that Tjf ∈ C(T n), 1 ≤ j ≤ 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).
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任意维环面上光滑函数空间中不存在局部无条件结构
考虑一个有限集合{T1,…, Tn (n≥2)上常系数微分算子的TJ},以及由该集合生成的光滑函数的空间,即Tjf∈C(Tn), 1≤j≤j的函数f的空间。我们证明了如果在它们的高级部分中至少有两个线性无关的算子(相对于某种同质性的混合模式),则该空间不具有局部无条件结构。这一事实推广了先前已知的结果,即这些空间不同构于C(S)的补子空间。
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来源期刊
Studia Mathematica
Studia Mathematica 数学-数学
CiteScore
1.50
自引率
12.50%
发文量
72
审稿时长
5 months
期刊介绍: The journal publishes original papers in English, French, German and Russian, mainly in functional analysis, abstract methods of mathematical analysis and probability theory.
期刊最新文献
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