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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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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

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.
References
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Bibliographic Information
  • Pavlos Motakis
  • Affiliation: Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario M3J 1P3, Canada
  • MR Author ID: 1037097
  • Email: pmotakis@yorku.ca
  • Received by editor(s): October 20, 2021
  • Published electronically: July 10, 2023
  • Additional Notes: The author was supported by NSERC Grant RGPIN-2021-03639.
  • © Copyright 2023 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 37 (2024), 1-37
  • MSC (2020): Primary 46B07, 46B25, 46B28, 46J10
  • DOI: https://doi.org/10.1090/jams/1024
  • MathSciNet review: 4654606