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Bull. Korean Math. Soc. 2017; 54(2): 443-454

Online first article March 13, 2017      Printed March 31, 2017

https://doi.org/10.4134/BKMS.b160011

Copyright © The Korean Mathematical Society.

$q$-frequent hypercyclicity in an algebra of operators

Jaeseong Heo, Eunsang Kim, and Seong Wook Kim

Hanyang University, Hanyang University, Hanyang University

Abstract

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We study a notion of $q$-frequent hypercyclicity of linear maps between the Banach algebras consisting of operators on a separable infinite dimensional Banach space. We derive a sufficient condition for a linear map to be $q$-frequently hypercyclic in the strong operator topology. Some properties are investigated regarding $q$-frequently hypercyclic subspaces as shown in \cite{BoGros2012}, \cite{Chan99} and \cite{CT2001}. Finally, we study $q$-frequent hypercyclicity of tensor products and direct sums of operators.

Keywords: hypercyclic operator, $q$-frequently hypercyclic operator, $q$-frequently hypercyclic subspace, strong operator topology

MSC numbers: 47A16

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