关于算子族的复杂性（英文）  

The Complexity on the Family of Operators

作　　者：姚玉武[1] 陈秀[1] 牛欣[1] 

机构地区：[1]合肥学院数学与物理系,安徽合肥230601

出　　处：《应用数学》2016年第3期649-655,共7页Mathematica Applicata

基　　金：Supported by the Science Foundation of Department of Education of Anhui Province(KJ2015A253);Anhui Leading Academic Discipline Project(2014xk08)

摘　　要：本文主要讨论Banach空间上有界线性算子族的复杂性,刻画具有稠密G_δ共同超循环向量集的算子族,推广Kit C.Chan和Rebecca Sanders的结果.作为应用,证明算子族{λB:λ∈Λ}的共同超循环向量集是一个稠密的G_δ集,这里B是单边移位算子,Λ是C的一个有界闭子集,满足λ∈Λ,|λ|>1.In this paper the complexity about the family of bounded linear operators is discussed. We first give a characterization about a family of operators on Banach space to have a dense G_δ set common hypercyclic vectors, which generalize Kit C. Chan and Rebecca Sanders＇ s results. Then as an application, we show that the set of all common hypercyclic vectors for the family {λB ： λ ∈ Λ} is a dense Gδset, where B is the unilateral backward shift and Λ is a bounded, closed subset of C with λ ∈ Λ, ｜λ｜ 1.

关 键 词：BANACH空间 超循环算子 移位算子 共同超循环向量 

分 类 号：O177.1[理学—数学] O19[理学—基础数学]