A relationship between the space of orthomorphisms and the centre of a vector lattice revisited
type: Item
instance of: scholarly article
title: A relationship between the space of orthomorphisms and the centre of a vector lattice revisited
zbMATH Open document ID: 1354.46006
published in: Positivity
publication date: 2016-06-10T00:00:00Z
review text: 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.
reviewed by: Beloslav Riečan
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 06F20
zbMATH DE Number: 6591947
zbMATH Keywords: center of a vector lattice
zbMATH Keywords: orthomorphism
author: Mohamed Ali Toumi
MaRDI profile type: Publication
full work available at URL: s11117-015-0358-0
OpenAlex ID: W1062852496
cites work: Q3748810
cites work: Sur les endomorphismes conservant les polaires d'un groupe réticulé archimédien
cites work: Multiplication operators
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cites work: Q5638775
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cites work: When orthomorphisms are in the ideal center
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cites work: The problem of central orthomorphisms in a class of \(F\)-lattices
DOI: 10.1007/S11117-015-0358-0
description: scientific article; zbMATH DE number 6591947