Abstract
The main topic of the present paper is a systematic investigation of the second order dual A″ of an Archimedean ƒ-algebra A with point separating order dual A′. It is shown that in the case that A has a unit element, the equality A″ = ( A′)′ n holds, where ( A′)′ n is the collection of all order continuous linear functionals on A′. It turns out that in general ( A′)′ n , equipped with the Arens multiplication is an ƒ-algebra again. Necessary and sufficient conditions are derived for ( A′)′ n to be semiprime and for ( A′)′ n to have a unit element with respect to this multiplication.
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