加权空间l~2(Z,a)上左移位算子的超循环性

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.

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

We first considered the bilateral weighted backward shift BW acting on the weighted spaces l2(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 λB which were supercyclic on l2(Z,a) .Then,we considered the hypercyclic vectors of B and BW acting on l2(Z,a),and gave some relationships between the hypercyclic vectors and weight sequence a = { an} n∈Z .