I'm having a hard time finding a solution for the following problem:

Prove that the operator $ T \in \mathcal{L}(\ell\_2) $ defined with the formula
$$ T((x\_1, x\_2, \dots, )) = (0, x\_1, x\_2/2, x\_3/3, \dots) $$

is compact. 

That's the trouble I'm having with functional analysis - how do I ever know how to approach a problem like this? I'm supposed to show that $T$ turns bounded sets into relatively compact sets (it's enough that it does so for a unit ball). However I can't seem to find a way to solve that