Wickstead's Conjecture on Positive Projections

For a positive projection $P$ on a Dedekind complete Banach lattice whose largest central operator below $P$ is $\alpha\,\mathrm{id}$, Wickstead conjectured $\alpha$ must be $0$ or $1/n$ for some natural $n$, 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.

Result

Proved

Status

Resolved

AI contribution

AI-assisted

Method

Argument

Field

Banach lattices

Posed by

Anthony W. Wickstead

Year posed

—

Years open

—

Solved

2026-04-16

Model

Claude Opus 4.6

Vendor

Anthropic

Collaborators

David Muñoz-Lahoz

Verification

Unreviewed

Publication

Preprint

Significance

12 / 100*

Disclosed cost

—

Wikipedia

No dedicated article