Dear Colleagues,

Could you please help me in solving this problem:

Find the norm of the linear functional $\displaystyle f$ defined on $\displaystyle C[-1,1]$ by $\displaystyle f(x)=\int_{-1} ^{0} x(t)dt-\int_{0} ^{1} x(t)dt$.

I have already proved that $\displaystyle ||f||\leq 2$, it remain to show that $\displaystyle ||f||\geq 2$.

Remark $\displaystyle ||x||=max \ x(t), t\in [-1,1]$.

Regards,

Raed.