Revista de la
Unión Matemática Argentina
Recurrence for weighted pseudo-shift operators
Mohamed Amouch and Fatima-ezzahra Sadek

Volume 68, no. 2 (2025), pp. 775–786    

Published online (final version): October 29, 2025

https://doi.org/10.33044/revuma.4120

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Abstract

We provide a characterization of multiply recurrent operators that act on a Fréchet space. As an application, we extend the weighted shift results established by Costakis and Parissis (2012). We achieve this by characterizing topologically multiply recurrent pseudo-shifts acting on an $F$-sequence space indexed by an arbitrary countable infinite set. This characterization is in terms of the weights, the OP-basis and the shift mapping. Additionally, we establish that the recurrence and the hypercyclicity of pseudo-shifts are equivalent.

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