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Journal of Operator Theory

Volume 71, Issue 2,  Spring  2014  pp. 427-453.

Strongly $n$-supercyclic operators

Authors:  Romuald Ernst
Author institution:Laboratoire de Mathematiques (UMR 6620) de l'Universite Blaise Pascal, Complexe universitaire des Cezeaux, 63171 Aubiere Cedex, France

Summary: In this paper, we are interested in the properties of a new class of operators, recently introduced by Shkarin, called strongly $n$-supercyclic operators. This notion is stronger than $n$-supercyclicity. We prove that such operators have interesting spectral properties and we give examples and counter-examples answering some questions asked by Shkarin.

Keywords: strongly n-supercyclic, n-supercyclic, hypercyclic

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