Geodesic
Order bounded orthosymmetric bilinear operator
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 873-880

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It is proved by an order theoretical and purely algebraic method that any order bounded orthosymmetric bilinear operator $b\colon E\times E\rightarrow F$ 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.
DOI : 10.1007/s10587-011-0052-8
Classification : 06F25, 46A40, 47A65
Keywords: vector lattice; positive bilinear operator; orthosymmetric bilinear operator; lattice bimorphism 
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Chil, Elmiloud. Order bounded orthosymmetric bilinear operator. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 4, pp. 873-880. doi: 10.1007/s10587-011-0052-8

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