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Let $X$ be a Banach space with $\dim X>1$ such that $X^{\ast}$, its dual, isseparable and $\mathcal{B}(X)$ the algebra of bounded linear operators on $X$.In this paper, we study the passage of property of being supercyclic from anoperator $T\in\mathcal{B}(X)$ to the left and right multiplication induced by$T$ on separable admissible Banach ideal of $\mathcal{B}(X)$. We give asufficient condition for the tensor product $T\widehat{\otimes}R$ of twooperators to be supercyclic. As a consequence, we give another equivalentconditions for the Supercyclicity Criterion.

Supercyclicity of the left and right multiplication operators on Banach ideal of operators