Topologically Multiply $\mathcal F$-Recurrent Operators in the Context of Locally Compact Hypergroups


Seyyed Mohammad Tabatabaie, Alireza Bagheri Salec, Sarah Nahed AbdulAbbas Al-Mamoori




Here we introduce topologically multiply $\mathcal F$-recurrent collections $\{T_t\}_{t\in S}$ of bounded linear operators on a Banach space $X$, where $\mathcal F$ is a Furstenberg family for a semigroup $S$. Then, we give some equivalent conditions for a collection $\{T_{a_t,w_t}\}_{t\in S}$ of weighted translation operators on an Orlicz space in the context of a locally compact hypergroup to be topologically multiply $\mathcal F$-recurrent.