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Primariness of the Mixed-Norm Space L_p(L_1)

Analysis · posed by Lechner, Motakis, Müller and Schlumprecht · solved

1 attempt

Statement

A Banach space is primary if in every decomposition into two complemented subspaces one summand is isomorphic to the whole. Lechner, Motakis, Müller and Schlumprecht identified the primariness of Lp(L1)L_p(L_1) as a prominent remaining open case; the paper proves it is primary for 1<p<1<p<\infty.

Context

Named by the authors of the preceding work as one of the prominent remaining open cases in the primariness programme.

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1 attempt

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  • #1

    Attempt 1

    proof attemptChatGPT 5.5 Pro with Antonio Acuaviva, Pablo Acuaviva ·
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    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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