Let $T:l^2 \to l^2$ be $T(a_1,a_2,...)=(a_2,a_3,...)$. Is this linear operator compact. If yes, how to prove it? If no, please give an example.
I want to show that if $(a_2,a_3,...)$ has a cluster point or not. I think it is sufficient to show that if $(a_1,a_2,...)\in l^2$ , does it have a cluster point?