Solution
= Solution
$\|T_hf\|_\infty\le\|h\|_\infty\|f\|_\infty$, so $T_h$ is bounded, and $h\mapsto T_h$ is linear with operator norm at most one.
= Solution
$\|T_hf\|_\infty\le\|h\|_\infty\|f\|_\infty$, so $T_h$ is bounded, and $h\mapsto T_h$ is linear with operator norm at most one.