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A Unital Banach Algebra That Is Not a Calkin Algebra

Analysis · posed by Tomasz Kania · solved

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Statement

The realisation problem asks which unital Banach algebras arise as the Calkin algebra B(X)/K(X)\mathcal{B}(X)/\mathcal{K}(X) of some Banach space. Recorded in Tarbard's thesis and studied by Horváth and Kania. The paper exhibits a unital Banach algebra that cannot be one.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Antonio Acuaviva and Pablo Acuaviva, using ChatGPT 5.5 Pro

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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    ai co developed
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    ChatGPT 5.5 Pro, driven directly and through Codex agents over a filesystem, generated the key ideas and the proof; the authors verified and refined it. The paper reports that the model sometimes misattributed a theorem, cited a result imprecisely, or presented steps as immediate when they still needed checking, so the human verification was load-bearing. The authors state none of these results came from the newer generation of models.

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