Some Remarks on Distributional Chaos for Linear Operators (Communications in Mathematical Research, 2021)
In this paper, we consider some properties for bounded linear operatorsconcerning distributional chaos. Norm-unimodality of bounded linear operators implies distributional chaos. Some properties such as similarity and spectra descriptionfor norm-unimodal operators are considered. The existence of distributional chaos innest algebra is also proved. In addition, we obtain a sufficient and necessary conditionof distributional chaos for a class of operators, which contains unilateral backwardweighted shift operators.