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Wickstead's Conjecture on Positive Projections

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wickstead-positive-projectionsAnalysisposed by Anthony W. Wicksteadrecorded: solved

1 attempt · no person has looked

Statement

For a positive projection PP on a Dedekind complete Banach lattice whose largest central operator below PP is α id\alpha\,\mathrm{id}, Wickstead conjectured α\alpha must be 00 or 1/n1/n for some natural nn, and proved the finite-dimensional case. The paper proves the conjecture in general and settles the representation problem for Banach lattice algebras as a consequence.

Context

A named Wickstead conjecture in positivity/Banach lattice theory, current enough to have its own workshop problem session, with a specialist audience.

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  • #1

    Attempt 1

    proof attemptClaude Opus 4.6 with David Muñoz-Lahoz ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    Claude Opus 4.6
    people
    David Muñoz-Lahoz

    The acknowledgments thank Claude Opus 4.6 "for providing the details of 4.2" - a specific proposition's proof details. The problem had its own session at a February 2026 workshop on Banach lattices.

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