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It is proved that for every compact metric space $K$ there exists a Banachspace $X$ whose Calkin algebra $\mathcal{L}(X)/\mathcal{K}(X)$ ishomomorphically isometric to $C(K)$. This is achieved by appropriatelymodifying the Bourgain-Delbaen $\mathscr{L}_\infty$-space of Argyros and Haydonin such a manner that sufficiently many diagonal operators on this space arebounded.

Separable Spaces of Continuous Functions as Calkin Algebras