A very simple example is given by $T(x) = 0$ for all $x \in [0,1]$.

Then $\Phi(f) = f(0) \cdot 1$ for all $f \in C([0,1])$, where $1$ denotes the constant function with value $1$. So $\Phi$ is a rank-$1$ projection and we thus have $\sigma(\Phi) = \{0,1\}$.