Grobler, J. J. Commutativity of the Arens product in lattice ordered algebras. (English) Zbl 0945.46003 Positivity 3, No. 4, 357-364 (1999). A lattice ordered algebra \(A\) is considered, i.e. \(A\) is a vector lattice and an associative algebra such that \(xy\geq 0\) whenever \(x\geq 0\), \(y\geq 0\). Denote by \(A'\) the band of all order bounded linear functionals on \(A\) and by \((A')_n'\) the band of all order bounded order continuous linear functionals on \(A'\). The author shows that \((A')_n'\) is Abelian whenever \(A\) is Abelian. The proof is based on an approximation of positive elements in \((A')_n'\) by elements in the canonical image \(\widehat A\) of \(A\) in \((A')_n'\). Reviewer: B.Riečan (Bratislava) Cited in 1 ReviewCited in 6 Documents MSC: 46A40 Ordered topological linear spaces, vector lattices 13J25 Ordered rings 46A20 Duality theory for topological vector spaces 06F25 Ordered rings, algebras, modules Keywords:order bounded linear functionals; lattice ordered algebra; order continuous linear functionals PDFBibTeX XMLCite \textit{J. J. Grobler}, Positivity 3, No. 4, 357--364 (1999; Zbl 0945.46003) Full Text: DOI