  It is proved that for every compact metric space $K$ there exists a Banach
space $X$ whose Calkin algebra $\mathcal{L}(X)/\mathcal{K}(X)$ is
homomorphically isometric to $C(K)$. This is achieved by appropriately
modifying the Bourgain-Delbaen $\mathscr{L}_\infty$-space of Argyros and Haydon
in such a manner that sufficiently many diagonal operators on this space are
bounded.
