A bounded linear operator $T$ from a Banach space $X$ to a Banach space $Y$ is called norm attaining, if there exist a vector $x\in X$ with $\|x\|=1$ such that
$$\|Tx\|=\|T\|.$$
Let $\mathbb{D}=\{z\in \mathbb{C}: |z|<1\}$. Consider the Disc Algebra $A(\mathbb{D}):=\{f\in\text{ Hol}(\mathbb{D}):f \text{ is continuous on }\overline{\mathbb{D}},~~\|f\|_{\infty}=\sup_{z\in\mathbb{D}}|f(z)|<\infty\}$.

Can we get a concrete example of non norm attaining bounded linear operator $T: A(\mathbb{D}) \longrightarrow A(\mathbb{D})$?