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arXiv · 2110.10868

Separable Spaces of Continuous Functions as Calkin Algebras

Pavlos Motakis
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Abstract

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.

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Pavlos Motakis. 2021-10-21. Separable Spaces of Continuous Functions as Calkin Algebras. https://doi.org/10.1090/jams%2F1024

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