Solution
= Solution
\b[No.] The point evaluations $\delta_x$ satisfy $\|\delta_x-\delta_y\|=2$ for $x\ne y$ (choose a <continuous function> taking values $1,-1$ at the two points). Thus $C[0,1]^*$ is nonseparable, whereas $\ell_1$ is separable.
= Solution
\b[No.] The point evaluations $\delta_x$ satisfy $\|\delta_x-\delta_y\|=2$ for $x\ne y$ (choose a <continuous function> taking values $1,-1$ at the two points). Thus $C[0,1]^*$ is nonseparable, whereas $\ell_1$ is separable.