加权空间l^2(Z,a)上左移位算子的超循环性  

The hypercyclicity and supercyclicity of backward shifts acting on the weighted spaces

作　　者：舒永录[1] 赵显锋[1] 何兴[1] 

机构地区：[1]重庆大学数学与统计学院,重庆400044

出　　处：《安徽大学学报（自然科学版）》2010年第6期13-16,共4页Journal of Anhui University(Natural Science Edition)

基　　金：重庆市自然科学基金资助项目(2009BB3185)

摘　　要：给出双边加权左移位算子BW在加权空间l2(Z,a)上是hypercyclic的一个充要条件(定理1),应用定理1的讨论方法,得到BW和λB是l2(Z,a)上的supercyclic算子的充要条件.再考虑加权空间上的算子B和BW的hypercyclic向量,给出了加权空间上移位算子的hypercyclic向量与权序列a={an}n∈Z之间存在的一些关系.We first considered the bilateral weighted backward shift Bw acting on the weighted spaces l^2（Z,a）.We proved that Bw was hypercyclic if and only if the weight sequence satisfied the conditions of Theorem 1. Based on Theorem 1 ,we gave the sufficient and necessary conditions about Bw and AB which were supercyclic on l^2（Z,a）.Then, we considered the hypercyclic vectors of B and Bw acting on l^2（Z ,a）, and gave some relationships between the hypercyclic vectors and weight sequence a={an}n∈Z.

关 键 词：hypercyclic算子 supercyclic算子 hypercyclic向量 

分 类 号：O117[理学—数学]