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Weakly Recurrent Operators

MEDITERRANEAN JOURNAL OF MATHEMATICS(2023)

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Abstract
In this paper, we introduce and study the notion of weak recurrence on a Banach space X . In one hand, we prove some properties of this class of operators. On the other hand, we study the weak recurrence of power bounded and diagonal operators. This leads us to deduce the relationship between this notion and other notion in linear dynamics.
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Key words
Hypercyclicity,supercyclicity,recurrence,weak hypercyclicity,weak supercyclicity
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