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Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 873-880, 2011
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Order bounded orthosymmetric bilinear operator

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Elmiloud Chil

* E. Chil*, Institut préparatoire aux études d'ingenieurs de Tunis, 2 Rue Jawaher Lel Nehrou 1008, Montfleury, Tunisia, e-mail: ` Elmiloud.chil@ipeit.rnu.tn`

**Abstract:** It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator $b E\times E\rightarrow F$ where $E$ and $F$ are Archimedean vector lattices is symmetric. This leads to a new and short proof of the commutativity of Archimedean almost $f$-algebras.

**Keywords:** vector lattice, positive bilinear operator, orthosymmetric bilinear operator, lattice bimorphism

**Classification (MSC 2010):** 06F25, 46A40, 47A65

**Full text** available as PDF.

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