Elmiloud Chil, Mohamed Mokaddem, Bourokba Hassen
Orthosymmetric bilinear map on Riesz spaces

Comment.Math.Univ.Carolin. 56,3 (2015) 307-317.

Abstract: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 [{\it On orthosymmetric bilinear maps\/}, Positivity {\bf 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 [{\it Homogeneous orthogonally additive polynomials on Banach lattices\/}, Bulletin of the London Mathematical Society {\bf 38} (2006), no.~3 123--134].

Keywords: orthosymmetric multilinear map; homogeneous polynomial; Riesz space

DOI: DOI 10.14712/1213-7243.2015.132
AMS Subject Classification: 06F25 46A40