Summary: Let \(X\) be a Banach space, \(\mathcal{B}(X)\) the algebra of bounded linear operators on \(X\) and \((J,\|{\cdot}\|_{J})\) an admissible Banach ideal of \(\mathcal{B}(X)\). For \(T\in\mathcal{B}(X)\), let \(L_{J,T}\) and \(R_{J,T}\in\mathcal{B}(J)\) denote the left and right multiplication defined by \(L_{J,T}(A)=TA\) and \(R_{J,T}(A)=AT\), respectively. In this paper, we study the transmission of some concepts related to recurrent operators between \(T\in\mathcal{B}(X)\), and their elementary operators \(L_{J,T}\) and \(R_{J,T}\). In particular, we give necessary and sufficient conditions for \(L_{J,T}\) and \(R_{J,T}\) to be sequentially recurrent. Furthermore, we prove that \(L_{J,T}\) is recurrent if and only if \(T\oplus T\) is recurrent on \(X\oplus X\). Moreover, we introduce the notion of a mixing recurrent operator and we show that \(L_{J,T}\) is mixing recurrent if and only if \(T\) is mixing recurrent.