Problems / analysis

analysis / Banach lattices

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.