Is this linear functional bounded? Find the norm. $$\ell^2\ni (x_n)\rightarrow2x_{1}+28x_2+35 x_{3}$$
I think it can be bounded:
$$|2x_{1}+28x_2+35 x_{3}| \le |2x_{1}|+|28x_2|+|35 x_{3}| \le 65 (\sum_{n=0}^{\infty}|x_n|^2)^{1/2}$$
But I can't find norm.

Because the dual space of $l^2$ is $l^2$.
