Characterization of separating couples |
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Authors: | Email author" target="_blank">Nedra?ToumiEmail author |
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Institution: | (1) Départment des Mathématiques, Faculté des Sciences de Bizerte, 7021 Zarzouna, Bizerte, Tunisia |
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Abstract: | Let A, B be two archimedean ℓ-algebras and let U,V be two positive linear maps from A to B. We call that the couple (U,V) is separating with respect to A and B if |a||b| = 0 in A implies |U (a)||V (b)| = 0 in B. In this paper, we prove that if A is an f-algebra with unit elment e, if B is an ℓ-algebra and if (U,V) is a separating couple with respect to A and B then (U
∼∼,V
∼∼), where U
∼∼ (resp V
∼∼) is the bi-adjoint of U (resp of V), is again a separating couple with respect to the order continuous order biduals (A′)′
n
and (B′)′
n
of A and B respectively furnished with their Arens products respectively. Moreover, in the case where B′ separates the points of B, we give a characterization of any separating couple with respect to A and B.
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Keywords: | Arens product ℓ -algebras f-algebras Separating couple |
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