Separable spaces of continuous functions as Calkin algebras

Motakis, Pavlos

doi:10.1090/jams/1024

Separable spaces of continuous functions as Calkin algebras
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by Pavlos Motakis

J. Amer. Math. Soc. 37 (2024), 1-37

DOI: https://doi.org/10.1090/jams/1024

Published electronically: July 10, 2023

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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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