Let A be a non-negative Toeplitz matrix, i.e. $a_{nk}$ >= 0 for all n,k. If $A_n(x)$= $\sum_{n} a_{nk}x_n$, where x is real, prove that
$$\liminf x_n \le \liminf A_n(x) \le \limsup A_n(x) \le \limsup x_n$$
I did not figure out how I can solve this problem, please help!!!!