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

Pub Date : 2021-04-07 DOI:10.4064/sm200629-21-12
A. Tselishchev
{"title":"Absence of local unconditional structure in spaces of smooth functions on the torus of arbitrary dimension","authors":"A. Tselishchev","doi":"10.4064/sm200629-21-12","DOIUrl":null,"url":null,"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).","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4064/sm200629-21-12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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).
分享
查看原文
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信