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Volume 27, Issue 4
Some Remarks on Distributional Chaos for Linear Operators

Geng Tian & Bingzhe Hou

Commun. Math. Res., 27 (2011), pp. 307-314.

Published online: 2021-05

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  • Abstract

In this paper, we consider some properties for bounded linear operators concerning distributional chaos. Norm-unimodality of bounded linear operators implies 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.

  • Keywords

distributional chaos, norm-unimodality, similarity, spectrum, nest algebra.

  • AMS Subject Headings

54H20, 37B99, 47A10, 47A99

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-307, author = {Tian , Geng and Hou , Bingzhe}, title = {Some Remarks on Distributional Chaos for Linear Operators}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {4}, pages = {307--314}, abstract = {

In this paper, we consider some properties for bounded linear operators concerning distributional chaos. Norm-unimodality of bounded linear operators implies 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.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19075.html} }
TY - JOUR T1 - Some Remarks on Distributional Chaos for Linear Operators AU - Tian , Geng AU - Hou , Bingzhe JO - Communications in Mathematical Research VL - 4 SP - 307 EP - 314 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19075.html KW - distributional chaos, norm-unimodality, similarity, spectrum, nest algebra. AB -

In this paper, we consider some properties for bounded linear operators concerning distributional chaos. Norm-unimodality of bounded linear operators implies 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.

Geng Tian & Bingzhe Hou. (2021). Some Remarks on Distributional Chaos for Linear Operators. Communications in Mathematical Research . 27 (4). 307-314. doi:
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