Some Remarks on Distributional Chaos for Linear Operators  

作　　者：TIAN GENG Hou BING-ZHE 

机构地区：[1]Institution of Mathematics, Jilin University, Changchun, 130012

出　　处：《Communications in Mathematical Research》2011年第4期307-314,共8页数学研究通讯（英文版）

基　　金：The Youth Foundation of Department of Mathematics,Jilin University

摘　　要：In this paper, we consider some properties for bounded linear operators concerning distributional chaos. Norm-unimodality of bounded linear operators im- plies distributional chaos. Some properties such as similarity and spectra description for norm-unimodal operators are considered. The existence of distributional chaos in nest algebra is also proved. In addition, we obtain a sufficient and necessary condition of distributional chaos for a class of operators, which contains unilateral backward weighted shift operators.In this paper, we consider some properties for bounded linear operators concerning distributional chaos. Norm-unimodality of bounded linear operators im- plies distributional chaos. Some properties such as similarity and spectra description for norm-unimodal operators are considered. The existence of distributional chaos in nest algebra is also proved. In addition, we obtain a sufficient and necessary condition of distributional chaos for a class of operators, which contains unilateral backward weighted shift operators.

关 键 词：distributional chaos norm-unimodality SIMILARITY SPECTRUM nest algebra 

分 类 号：O177.1[理学—数学] P413[理学—基础数学]