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Outline

Orthosymmetric bilinear map on Riesz spaces

2015, Commentationes Mathematicae Universitatis Carolinae

https://doi.org/10.14712/1213-7243.2015.132

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 × E → F is automatically symmetric. This generalizes in certain way an earlier result by F. Ben Amor [On orthosymmetric bilinear maps, Positivity 14 (2010), [123][124][125][126][127][128][129][130][131][132][133][134]. As an application, we show that under a certain separation condition, any orthogonally additive homogeneous polynomial P : E → F is linearly represented. This fits in the type of results by Y.

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