Orthosymmetric bilinear map on Riesz spaces

Commentationes mathematicae Universitatis Carolinae

Elmiloud Chil¹ 

关键词: orthosymmetric multilinear map;    homogeneous polynomial;    Riesz space;   

DOI  :  10.14712/1213-7243.2015.132

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

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 $TE\times E\rightarrow F$ 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 $PE\rightarrow F$ 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].

【 授权许可】

CC BY