Normed and Banach spaces

(Exam style.) On $\ell^2$, define the right shift $S(x_1, x_2, \dots) = (0, x_1, x_2, \dots)$ and $D(x_1, x_2, \dots) = (x_1, \frac{x_2}2, \frac{x_3}3, \dots)$. (a) Find $\|S\|$ and $\|D\|$. (b) Show $S$ is not compact. (c) Show $D$ is compact.