Orthosymmetric bilinear map on Riesz spaces

Elmiloud Chil; Mohamed Mokaddem; Bourokba Hassen

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 3, page 307-317
  • ISSN: 0010-2628

Abstract

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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 × E → F is automatically symmetric. This generalizes in certain way an earlier result by F. Ben Amor [On orthosymmetric bilinear maps, Positivity 14 (2010), 123–134]. 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. 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].

How to cite

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Chil, Elmiloud, Mokaddem, Mohamed, and Hassen, Bourokba. "Orthosymmetric bilinear map on Riesz spaces." Commentationes Mathematicae Universitatis Carolinae 56.3 (2015): 307-317. <http://eudml.org/doc/271613>.

@article{Chil2015,
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 [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].},
author = {Chil, Elmiloud, Mokaddem, Mohamed, Hassen, Bourokba},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {orthosymmetric multilinear map; homogeneous polynomial; Riesz space},
language = {eng},
number = {3},
pages = {307-317},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Orthosymmetric bilinear map on Riesz spaces},
url = {http://eudml.org/doc/271613},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Chil, Elmiloud
AU - Mokaddem, Mohamed
AU - Hassen, Bourokba
TI - Orthosymmetric bilinear map on Riesz spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 3
SP - 307
EP - 317
AB - 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].
LA - eng
KW - orthosymmetric multilinear map; homogeneous polynomial; Riesz space
UR - http://eudml.org/doc/271613
ER -

References

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