Extension of positive projections
type: Item
instance of: scholarly article
title: Extension of positive projections
zbMATH Open document ID: 1011.46005
DOI: 10.1007/BF02844428
author: Mohamed Ali Toumi
publication date: 2003-03-18T00:00:00Z
review text: Let \(P\) be a positive projection defined on a majorizing subspace \(A\) of a Dedekind complete vector lattice \(E\). For an element \(x_0\notin E\setminus A\) the author finds a necessary and sufficient condition for the existence of a positive extension to \([A,x_0]\) that is also a projection, where \([D]\) denotes the linear space generated by a subset \(D\) of \(E\). If \(x_0\) does not satisfy this condition, then there exists some \(y_0\in E\) such that \(P\) can be extended to a positive projection on \([A,x_0, y_0]\). The fact that \(P\) can be extended to a positive projection on \(E\) was proved earlier by \textit{K. Triki} [J. Math. Anal. Appl. 153, 486-496 (1990; Zbl 0727.47021)]. The proofs offered by the author do not use the axiom of choice.
Mathematics Subject Classification ID: 46A40
Mathematics Subject Classification ID: 46B40
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 1884312
zbMATH Keywords: positive projections
reviewed by: Y. A. Abramovich
MaRDI profile type: Publication
cites work: Q3748810
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1884312