Commutativity of the Arens product in lattice ordered algebras |
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Authors: | Grobler JJ |
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Institution: | (1) Department of Mathematics and Applied Mathematics, Potchefstroom University for CHE, Potchefstroom, 2520, South Africa |
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Abstract: | Let
be an Abelian Archimedean lattice ordered algebra. The order bidual
furnished with the Arens product is again a lattice ordered algebra. We show that the order continuous order bidual
is Abelian. This solves an open problem and improves a result of Scheffold, who proved it for the case of normed lattice ordered algebras. The proof is based on the up-down-up approximation of positive elements in the order continuous order bidual
by elements in the canonical image
of
in
Components of positive elements in
are characterized and the result is applied to the Arens product of
-and almost
-algebras. |
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Keywords: | Arens product
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-algebra Riesz algebra |
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