Bidual of r-algebras

Abstract

We prove that the order continuous bidual of an Archimedean r-algebra is a Dedekind complete r-algebra with respect to the Arens multiplications.

An almost orthosymmetric bilinear map

“…(B 0 ) 0 n is a positive almost orthosymmetric bilinear map. This also generalizes results on the order bidual of pseudo-almost f -algebras in [17].…”

“…In [17], concentrating on the Arens multiplications [2,3] in the algebraic bidual of pseudo-almost f -algebras (so-called r-algebra in [17]), we prove that the order continuous bidual of an Archimedean pseudo-almost f -algebra is again a Dedekind complete (and hence Archimedean) pseudo-almost f -algebra. This is a generalization of a result of Bernau and Huijsmans in [4] in which they prove that the order continuous bidual of an almost f -algebra (respectively d-algebra) is again an almost f -algebra (respectively d-algebra).…”