Czechoslovak Mathematical Journal, Vol. 61, No. 4, pp. 873-880, 2011

# Order bounded orthosymmetric bilinear operator

## 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

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