$q$-frequent hypercyclicity in an algebra of operators
Bull. Korean Math. Soc. 2017 Vol. 54, No. 2, 443-454
Published online March 13, 2017
Printed March 31, 2017
Jaeseong Heo, Eunsang Kim, and Seong Wook Kim
Hanyang University, Hanyang University, Hanyang University
Abstract : 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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