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arXiv · 0903.4558

Some dynamical properties for linear operators

Bingzhe Hou·Geng Tian·Luoyi Shi
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Abstract

In our another recent article, we introduce a new dynamical property for linear operators called norm-unimodality which implies distributional chaos. In the present paper, we'll give a further discussion of norm-unimodality. It is showed that norm-unimodality is similar invariant and the spectra of norm-unimodal operator is referred to. As an application, in each nest algebra there exist distributional chaotic operators. Moreover, normal operators and compact operators with regard to norm-unimodality and Li-Yorke chaos are also be considered. Specially, a small compact perturbation of the unit operator could be distributionally chaotic.

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Bingzhe Hou, Geng Tian, Luoyi Shi. 2009-03-26. Some dynamical properties for linear operators. https://arxiv.org/abs/0903.4558

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