Commutativity of the Arens product in lattice ordered algebras
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 \((A')_n'\).
scientific article; zbMATH DE number 1389560