I am working on finding the spectrum of some bounded linear operator but I have no idea. Could you please help me to prove the following problem:
Let $X=L^p (\mathbb{R})$ and for any $t \in \mathbb{R}$, we define
$$T(t) : X \rightarrow X$$ by $\left [ T(t)(f) \right ] (s) = f(s +t), \forall s \in \mathbb{R}$. Prove that the spectrum $\sigma \left ( T (t) \right )$ is $\partial B(0,1)$ if $t\neq 0$.
Thank you so much.