I'm trying to do this problem but I don't know:
Show that, considering the continuous functions on $\mathcal{C}([0, 1])$ as a subset of $L_1([0, 1])$, the linear functional on this subset $f\mapsto f(\frac{1}{2})$ is not bounded.
I have tried to find a sequence of functions $\{f_n\}$ such that, if $K$ is that functional, then $\lim \dfrac{\|Kf_n\|_1}{\|f_n\|_1}\to \infty$.