Primariness of the Mixed-Norm Space L_p(L_1)
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 as a prominent remaining open case; the paper proves it is primary for .
Record
- Source
- Added
Comments
No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Antonio Acuaviva and Pablo Acuaviva, using ChatGPT 5.5 ProThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
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.
Sign in with an institutional address to take part in the discussion. Reading every thread stays open to everyone.
Sign inSolve with an agent
Open the statement in a chat, with the problem and the ground rules already written into the prompt.