Consider the Banach space $B=C[-1,1]$, with $\sup$ norm, for $f\in B$ define $\tilde f(x)=f(|x|)$, $T:B\rightarrow B, T(f)=\tilde f$ we need to show $T$ is a bounded linear operator on $B$, what is $||T||?$
$T(cf+g)= (f+g)(|x|)=cf(|x|)+ g(|x|)=c\tilde f+\tilde g$ so $T$ is linear as we know continous functions over compact set is bounded so clearly $T$ is bounded?
I am not able to determine $||T||$.