Geodesic
Orthosymmetric bilinear map on Riesz spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 307-317.

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Let $E$ be a Riesz space, $F$ a Hausdorff topological vector space (t.v.s.). We prove, under a certain separation condition, that any orthosymmetric bilinear map $T:E\times E\rightarrow F$ is automatically symmetric. This generalizes in certain way an earlier result by F. Ben Amor [On orthosymmetric bilinear maps, Positivity 14 (2010), 123--134]. As an application, we show that under a certain separation condition, any orthogonally additive homogeneous polynomial $P : E\rightarrow F$ is linearly represented. This fits in the type of results by Y. Benyamini, S. Lassalle and J.L.G. Llavona [Homogeneous orthogonally additive polynomials on Banach lattices, Bulletin of the London Mathematical Society 38 (2006), no. 3 459--469].
DOI : 10.14712/1213-7243.2015.132
Classification : 06F25, 46A40
Keywords: orthosymmetric multilinear map; homogeneous polynomial; Riesz space 
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Chil, Elmiloud; Mokaddem, Mohamed; Hassen, Bourokba. Orthosymmetric bilinear map on Riesz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 307-317. doi : 10.14712/1213-7243.2015.132. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.132/

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