A Note About Sensitivity and Transitive Sensitivity for Linear Operators  

关于线性算子的敏感和传递敏感的一个注记

作　　者：YAO Quanquan ZHU Peiyong 姚权权;朱培勇(电子科技大学数学科学学院,四川成都611731)

机构地区：[1]School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu,Sichuan,611731,P.R.China

出　　处：《数学进展》2024年第6期1271-1284,共14页Advances in Mathematics（China）

基　　金：Supported by NSFC (No.11501391)。

摘　　要：Let(X,T) be a linear dynamical system,where X is a Banach space over C and T:X→X is a bounded linear operator.We show that if(X,T) is sensitive and not cofinitely sensitive,then σ(T) ∩T≠?,where σ(T) is the spectrum of T and T={λ∈C:|λ|=1},and that there is a non-hypercyclic,sensitive system(X,T) which is not syndetically sensitive.We also show that there is a transitively sensitive system(X,T) which is mean sensitive but not multi-transitively sensitive.设(X,T)为一个线性动力系统,其中X是一个复数域上的Banach空间和T:X→X是一个有界线性算子.本文证明了若(X,T)敏感但非余有限敏感,则σ(T)∩T≠?,其中σ(T)是算子T的谱集和T={λ∈C:|λ|=1},并且给出了一个非超循环、敏感但非syndetic敏感的系统.本文还给出了一个传递敏感、平均敏感但非多重传递敏感的系统.

关 键 词：sensitivity SPECTRUM transitive sensitivity syndetic sensitivity 

分 类 号：O177.2[理学—数学]