Hypercyclicity Properties of Commutator Maps

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• 作者：Clifford Gilmore ; Eero Saksman ; Hans-Olav Tylli
• 关键词：Hypercyclicity ; Commutator operators ; Multipliers ; Supercyclicity ; Linear dynamics
• 刊名：Integral Equations and Operator Theory
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：1
• 页码：139-155
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis;
• 出版者：Springer International Publishing
• ISSN：1420-8989
• 卷排序：87

文摘

We investigate the hypercyclic properties of commutator operators acting on separable Banach ideals of operators. As the main result we prove the commutator map induced by scalar multiples of the backward shift operator fails to be hypercyclic on the space of compact operators on \(\ell ^2\). We also establish several necessary conditions which identify large classes of operators that do not induce hypercyclic commutator maps.