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Centered orthomorphisms and the Wickstead problem
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DOI：10.1007/s11117-026-01187-7.png)
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Abstract
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In this paper we prove that for (ru)-complete semiprime f-algebras with weak order units, A is a Banach lattice if and only if Orth(A)=Stab(A)=Z(A)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Orth(A)=Stab(A)=Z(A)$$\end{document}. This answers a natural question posed by Wickstead in [W & oacute;jtowicz, M., Wisniewska, H.: The problem of central orthomorphisms in a class of F-lattices. Indag. Math. New Ser. 26(2), 393-403 (2015)]. The inspiration for this characterization arises from a rigorous study of finite elements in Archimedean vector lattices. Furthermore, by introducing a new class of orthomorphisms, termed pseudo-center, we affirmatively solve its related Wickstead problem.
Keywords:
Orthomorphism
Center
Stabilizer
Pseudo-center
Finite element
Totally finite element
Self-majorizing element