Consider $T: (C[-1,1],\|\cdot\|_{2})\rightarrow \mathbb{C}\\Tf :=\int_{-1}^{1}mf\,\mathrm{d}x$ where $m\in C[-1,1]$.
I want to prove $\|T\| = \|m\|_2$.
$\|T\|\leq\|m\|_2$ can be easily proved by Hölder's inequality, how to solve $\|T\|\geq\|m\|_{2}$?
Thank you.