  Let $X$ be a Banach space with $\dim X>1$ such that $X^{\ast}$, its dual, is
separable 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 an
operator $T\in\mathcal{B}(X)$ to the left and right multiplication induced by
$T$ on separable admissible Banach ideal of $\mathcal{B}(X)$. We give a
sufficient condition for the tensor product $T\widehat{\otimes}R$ of two
operators to be supercyclic. As a consequence, we give another equivalent
conditions for the Supercyclicity Criterion.
