I need help from someone to solve this problem.
Given a bounded sequence $(\lambda_n)$ in $\mathbb С$ define an operator $S$ in $B(\ell_2)$ by $S(x_1) = 0$ and $S(x_n) = \lambda_n x_{n-1}$ , $n > 1$, for $x = (x_n) \in \ell_2$. Find the polar decomposition of $S$, and characterize those sequences $\{\lambda_n\}$ in $\ell_\infty$ for which $S$ is compact.