紧算子理想中d维流的遍历定理

A. Azizov
{"title":"紧算子理想中d维流的遍历定理","authors":"A. Azizov","doi":"10.56017/2181-1318.1150","DOIUrl":null,"url":null,"abstract":"Let H be an infinite-dimensional complex Hilbert space, let (B(H), ‖ · ‖∞) be the C?-algebra of all bounded linear operators acting in H, and let CE be the symmetric ideal of compact operators in H generated by the fully symmetric sequence space E ⊂ c0. If Tu : B(H) → B(H), u = (u1, . . . , ud) ∈ R+, is a semigroup of positive Dunford-Schwartz operators, which is strongly continuous on C1, then the following versions of individual and mean ergodic theorems are true: For each x ∈ CE the net At(x) = 1 td ∫ [0,t]d Tu(x)du, t > 0, converges to some x̂ ∈ CE with respect to the norm ‖ · ‖∞, as t → ∞; moreover, if E is separable and E 6= l1 (as a sets), then lim t→∞ ‖At(x)− x̂‖CE = 0.","PeriodicalId":127023,"journal":{"name":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Ergodic theorems for d-dimensional flows in ideals of compact operators\",\"authors\":\"A. Azizov\",\"doi\":\"10.56017/2181-1318.1150\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let H be an infinite-dimensional complex Hilbert space, let (B(H), ‖ · ‖∞) be the C?-algebra of all bounded linear operators acting in H, and let CE be the symmetric ideal of compact operators in H generated by the fully symmetric sequence space E ⊂ c0. If Tu : B(H) → B(H), u = (u1, . . . , ud) ∈ R+, is a semigroup of positive Dunford-Schwartz operators, which is strongly continuous on C1, then the following versions of individual and mean ergodic theorems are true: For each x ∈ CE the net At(x) = 1 td ∫ [0,t]d Tu(x)du, t > 0, converges to some x̂ ∈ CE with respect to the norm ‖ · ‖∞, as t → ∞; moreover, if E is separable and E 6= l1 (as a sets), then lim t→∞ ‖At(x)− x̂‖CE = 0.\",\"PeriodicalId\":127023,\"journal\":{\"name\":\"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.56017/2181-1318.1150\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56017/2181-1318.1150","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

设H为无穷维复希尔伯特空间,设(B(H),‖·‖∞)为C?作用于H中的所有有界线性算子的-代数,并设CE为由完全对称序列空间E∧c0生成的H中的紧算子的对称理想。若Tu: B(H)→B(H),则u = (u),…, d)∈R+,是在C1上强连续的正Dunford-Schwartz算子半群,则个别遍历定理和平均遍历定理的下列版本成立:对于每个x∈CE,净At(x) = 1 td∫[0,t]d Tu(x)du, t > 0,收敛于某x∈CE关于范数‖·‖∞,当t→∞;此外,如果E是可分离的,且e6 = l1(作为集合),则lim t→∞‖At(x)−x³‖CE = 0。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Ergodic theorems for d-dimensional flows in ideals of compact operators
Let H be an infinite-dimensional complex Hilbert space, let (B(H), ‖ · ‖∞) be the C?-algebra of all bounded linear operators acting in H, and let CE be the symmetric ideal of compact operators in H generated by the fully symmetric sequence space E ⊂ c0. If Tu : B(H) → B(H), u = (u1, . . . , ud) ∈ R+, is a semigroup of positive Dunford-Schwartz operators, which is strongly continuous on C1, then the following versions of individual and mean ergodic theorems are true: For each x ∈ CE the net At(x) = 1 td ∫ [0,t]d Tu(x)du, t > 0, converges to some x̂ ∈ CE with respect to the norm ‖ · ‖∞, as t → ∞; moreover, if E is separable and E 6= l1 (as a sets), then lim t→∞ ‖At(x)− x̂‖CE = 0.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
ASYMPTOTIC RESULTS FOR EMPIRICAL PROCESSES IN INFORMATIVE MODEL OF RANDOM CENSORSHIP FROM BOTH SIDES Local and 2-local derivations on small dimensional Zinbiel algebras On the Hartogs theorem for A-analytic functions in ℂn DUALITY FOR L1-SPACES ASSOCIATED WITH THE MAHARAM MEASURE NUMERICAL CALCULATION OF LYAPUNOV STABLE SOLUTIONS OF THE HYPERBOLIC SYSTEMS
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1