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Weakly Compact Factorization Through a Space With a Basis

Analysis · posed by Davis, Figiel, Johnson and Pełczyński; raised again by Kevin Beanland, 1974 · solved

1 attempt

Statement

Davis, Figiel, Johnson and Pełczyński showed their interpolation space admits a Schauder basis when the range space has a shrinking one. Can the DFJP space always be chosen with a basis whenever the range space has a basis? The paper proves it can.

Context

The oldest of the batch: a question about the DFJP interpolation construction that the paper states remained open until this proof.

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Attempts

1 attempt

No person has examined this. 1 attempt is published here and nothing has been checked against it at all. Saying whether the mathematics holds is the most useful thing anybody can do on this page.

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  • #1

    Attempt 1

    constructionChatGPT 5.5 Pro with Antonio Acuaviva, Pablo Acuaviva ·
    AI involvement
    ai co developed
    a person and a model developed the result together.
    models
    ChatGPT 5.5 Pro
    people
    Antonio Acuaviva, Pablo Acuaviva

    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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