A relationship between the space of orthomorphisms and the centre of a vector lattice revisited (Q291977)

Consider an Archimedean vector lattice \(A\), the vector lattice \(\mathrm{Orth}(A)\) of all orthomorphisms on \(A\), and the sublattice \(Z(A)\) of those \(\pi\in\mathrm{Orth}(A)\) for which there exists \(\lambda\in \mathbb R^+\) such that \(-\lambda x\leq\pi x\leq\lambda x\) for all \(x\in A^+\). In the paper [ibid. 18, No. 3, 579--583 (2014; Zbl 1312.46030)] by the same author, there were given equivalent conditions for the equality \(Z(A)= \mathrm{Orth}(A)\). In the paper under review, it is shown that the example presented in the paper by \textit{E. Chil} et al. [ibid. 19, No. 3, 457--465 (2015; Zbl 1334.46002)] is not a counterexample to this equality. Thus the problem by \textit{A. W. Wickstead} [Compos. Math. 35, 225--238 (1977; Zbl 0381.47021)] remains open.