关于Syndetic敏感和Multi敏感在Frechet空间的一个注记  

A Note About Syndetic Sensitivity and Multi-Sensitivity on Frechet Space

作　　者：姚权权 朱培勇[1] Yao Quanquan;Zhu Peiyong(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu 611731)

机构地区：[1]电子科技大学数学科学学院,成都611731

出　　处：《数学物理学报（A辑）》2020年第4期1061-1071,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11501391)。

摘　　要：设(X,T)为动力系统,其中X是可分的Frechet空间和T:X→X是算子,首先证明了以下命题等价:(1)(X,T)是敏感的;(2)(X,T)是multi敏感;(3)(X,T)是multi-thick敏感;(4)(X,T)是thick敏感.不仅如此,还证明了如下命题:(X,T)是syndetic敏感当且仅当(X,T)是thickly syndetic敏感.如果(X,T)是syndetic传递,那么(X,T)是syndetic敏感.如果(X,T)是F-超循环,那么(X,T)是thickly syndetic敏感.如果(X,T)是syndetic传递,那么(X,T)是传递敏感.最后证明了迭代动力系统也有类似的结果.Let(X,T)be a linear dynamical system,where X is a separable Frechet space and T:X→X is a operator.first we prove the following assertions are equivalent:(1)(X,T)is sensitive;(2)(X,T)is multi-sensitive;(3)(X,T)is multi-thickly-sensitive;(4)(X,T)is thickly sensitive.Then we prove the following propositions:(X,T)is syndetically sensitive if and only if(X,T)is thickly syndetically sensitive.If(X,T)is syndetic transitive,then(X,T)is syndetically sensitive.If(X,T)is frequently hypercyclic,then(X,T)is thickly syndetically sensitive.If(X,T)is syndetically transitive,then(X,T)is transitively sensitive.Moreover,the iterated function system has the similar results.

关 键 词：Multi敏感 Thickly Syndetic敏感 迭代动力系统 

分 类 号：O189.11[理学—数学]