Let $X$ be a Banach space with the $L^{\infty}$ norm and let $A$: $X \rightarrow X$ be an integral operator of the following form,
\begin{equation} Ax(s) = \lambda\int^{b}_{a}K(s,t)x(t)dt, \end{equation} where $K$: $[a,b] \times [a,b]\rightarrow \mathbb{R}$ is a continuous map such that $K \neq 0$ and where $\lambda$ is a constant.
I know that due to the continuity of $K$, Arzelà–Ascoli theorem implies that $A$ is compact. But in the uploaded image they say $A$ is Fredholm as well. I fail to see why, could someone help me out?
