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

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.