Li-Yorke chaos translation set for linear operators

In order to study Li-Yorke chaos by the scalar perturbation for a given bounded linear operator \(T\) on Banach spaces \(X\), we introduce the Li-Yorke chaos translation set of \(T\), which is defined by \(S_{LY}(T)=\{\lambda\in\mathbb{C};\lambda+T \text{ is Li-Yorke chaotic}\}\). In this paper, som...

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Hou, Bingzhe, Luo, Lvlin
Format: Article
Language:English
Subjects:
Banach spaces
Hilbert space
Linear operators
Perturbation
Online Access:Get full text
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Summary:In order to study Li-Yorke chaos by the scalar perturbation for a given bounded linear operator \(T\) on Banach spaces \(X\), we introduce the Li-Yorke chaos translation set of \(T\), which is defined by \(S_{LY}(T)=\{\lambda\in\mathbb{C};\lambda+T \text{ is Li-Yorke chaotic}\}\). In this paper, some operator classes are considered, such as normal operator, compact operator, shift and so on. In particular, we show that the Li-Yorke chaos translation set of Kalisch operator on Hilbert space \(\mathcal{L}^2[0,2\pi]\) is a simple point set \(\{0\}\).
ISSN:2331-8422