Geodesic
The triadjoint of an orthosymmetric bimorphism
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 85-94

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Let $A$ and $B$ be two Archimedean vector lattices and let $( A^{\prime }) _n'$ and $( B') _n'$ be their order continuous order biduals. If $\Psi \colon A\times A\rightarrow B$ is a positive orthosymmetric bimorphism, then the triadjoint $\Psi ^{\ast \ast \ast }\colon ( A') _n'\times ( A') _n'\rightarrow ( B') _n'$ of $\Psi $ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost $f$-algebras.
Let $A$ and $B$ be two Archimedean vector lattices and let $( A^{\prime }) _n'$ and $( B') _n'$ be their order continuous order biduals. If $\Psi \colon A\times A\rightarrow B$ is a positive orthosymmetric bimorphism, then the triadjoint $\Psi ^{\ast \ast \ast }\colon ( A') _n'\times ( A') _n'\rightarrow ( B') _n'$ of $\Psi $ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost $f$-algebras.
Classification : 06F25, 47B65
Keywords: almost $f$-algebra orthosymmetric bimorphism 
Toumi, Mohamed Ali. The triadjoint of an orthosymmetric bimorphism. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 1, pp. 85-94. http://geodesic.mathdoc.fr/item/CMJ_2010_60_1_a5/
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