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.
Jaeseong Heo, Eunsang Kim, and Seong Wook Kim
Hanyang University, Hanyang University, Hanyang University
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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