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2015 $q$-Frequently hypercyclic operators
Manjul Gupta, Aneesh Mundayadan
Banach J. Math. Anal. 9(2): 114-126 (2015). DOI: 10.15352/bjma/09-2-9


We introduce $q$-frequently hypercyclic operators and derive a sufficient criterion for a continuous operator to be $q$-frequently hypercyclic on a locally convex space. Applications are given to obtain $q$-frequently hypercyclic operators with respect to the norm-, $F$-norm- and weak*- topologies. Finally, the frequent hypercyclicity of the non-convolution operator $T_\mu$ defined by $T_\mu(f)(z)=f'(\mu z)$, $|\mu|\geq 1$ on the space $H(\mathbb{C})$ of entire functions equipped with the compact-open topology is shown.


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Manjul Gupta. Aneesh Mundayadan. "$q$-Frequently hypercyclic operators." Banach J. Math. Anal. 9 (2) 114 - 126, 2015.


Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1329.47007
MathSciNet: MR3296109
Digital Object Identifier: 10.15352/bjma/09-2-9

Primary: 47A16
Secondary: 46A45

Keywords: $q$-frequent hypercyclicity criterion , $q$-frequently hypercyclic operator , backward shift operator , unconditional convergence , ymmetric Schauder basis

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.9 • No. 2 • 2015
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