Hypercyclicity Properties of Commutator Maps

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http://hdl.handle.net/10138/312775

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Gilmore , C , Saksman , E & Tylli , H-O 2017 , ' Hypercyclicity Properties of Commutator Maps ' , Integral Equations and Operator Theory , vol. 87 , no. 1 , pp. 139-155 . https://doi.org/10.1007/s00020-016-2332-z

Title: Hypercyclicity Properties of Commutator Maps
Author: Gilmore, Clifford; Saksman, Eero; Tylli, Hans-Olav
Other contributor: University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
University of Helsinki, Department of Mathematics and Statistics
Date: 2017-01
Language: eng
Number of pages: 17
Belongs to series: Integral Equations and Operator Theory
ISSN: 0378-620X
DOI: https://doi.org/10.1007/s00020-016-2332-z
URI: http://hdl.handle.net/10138/312775
Abstract: 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 . We also establish several necessary conditions which identify large classes of operators that do not induce hypercyclic commutator maps.
Subject: Hypercyclicity
Commutator operators
Multipliers
Supercyclicity
Linear dynamics
NORMAL DERIVATIONS
OPERATOR ALGEBRA
SPACES
UNIVERSAL
111 Mathematics
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