Show that the inverse of the linear operator $\ell^\infty\to\ell^\infty:x\mapsto(x_j/j)_j$ is not bounded

Show that the operator $l^{\infty }\rightarrow l^{\infty } $ defined by $y=(\eta _{j})=Tx$, $\eta _{j}=\frac{\xi _{j}}{j}$, $x=\xi _{j}$ has inverse operator not bounded.

I though by continuity, (continuity if and only if is bounded) or can it resolved by continuity in a point?