Some Remarks on Distributional Chaos for Linear Operators 被引量：1

Some Remarks on Distributional Chaos for Linear Operators

下载PDF

导出

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.

作者 TIAN GENG Hou BING-ZHE

机构地区 Institution of Mathematics

出处《Communications in Mathematical Research》 CSCD 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

关键词 distributional chaos norm-unimodality SIMILARITY SPECTRUM nest algebra distributional chaos, norm-unimodality, similarity, spectrum, nest algebra

分类号 O177.1 [理学—基础数学] P413 [天文地球—大气科学及气象学]

引文网络
相关文献

参考文献8

1Grosse-Erdmann, K. G., Recent developments in hypercyclicity, Rev. Real Acad. Cienc. Serie A. Mat., 97(2003), 273-286.
2Shapiro, J. H., Notes on Dynamics of linear operators, unpublished Lecture Notes, Available at http://www.math.msu.edu/~shapiro.
3Schweizer, B. mad Smital, J., Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc., 344(1994), 737-754.
4Martfnez-Gim~nez, F., Oprocha, P. and Peris, A., Distributional chaos for backward shifts, J. Math. Anal. Appl., 351(2009), 607-615.
5Hou, B. Z., Cui, P. and Cao, Y., Chaos for Cowen-Douglas operators, Proc. Amer. Math. Soc., 138(2010), 929-936.
6Hou, B. Z., Tian, G. and Zhu, S., Approximation of chaotic operators, J. Operator Theory, forthcoming.
7Li, Y., Tian, G., Wu, F. and Hou, B. Z., The existence of distributional chaos in nest algebras (in Chinese), J. Jilin Univ. (Science Edition), 47(2009), 948-950.
8Davidson, K. R., Nest Algebras, Longman Scientific ~ Technical, Essex, 1988.

引证文献1

1姚玉武,陈秀,牛欣.复扇形指标集上的分布混沌[J].数学物理学报（A辑）,2017,37(5):950-961.

1董延武.递归生成加权移位算子正的二次亚正规性[J].廊坊师范学院学报（自然科学版）,2013,13(5):12-16.
2丁宣浩,石刚.加权移位的乘积[J].四川大学学报（自然科学版）,1995,32(4):462-462.
3吕方.A_(■0)类移位的构造和Beurling格的一个性质[J].科学通报,1991,36(7):490-491.
4吉国兴.关于加权移位的几点注记[J].纯粹数学与应用数学,1989,5(5):12-15.
5YIN Jian-dong QIU Yu-fen.A Note on P-chaos Implies Distributional Chaos and Chaos in the Sense of Devaney with Positive Topological Entropy[J].Chinese Quarterly Journal of Mathematics,2013,28(2):269-273.
6姚玉武,史恩慧,周友成.Banach空间上的强混合算子[J].数学年刊（A辑）,2006,27(2):189-196. 被引量：5
7丁宣浩,石刚.加权移位算子的乘积[J].Journal of Mathematical Research and Exposition,1995,15(3):471-472.
8smail Aslan,Vangelis Marinakis.Some Remarks on Exp-Function Method and Its Applications[J].Communications in Theoretical Physics,2011,56(9):397-403.
9Rui Chang PEI.A Remark on the Generalized Second Order Toda System[J].Acta Mathematica Sinica,English Series,2013,29(9):1691-1702.
10钟光胜,田立新.加权移位算子的非游荡性[J].佳木斯大学学报（自然科学版）,2010,28(2):296-299.

Communications in Mathematical Research

2011年第4期

浏览历史

内容加载中请稍等...

Some Remarks on Distributional Chaos for Linear Operators 被引量：1

参考文献8

引证文献1

相关作者

相关机构

相关主题

浏览历史