| Title:
|
Orthosymmetric bilinear map on Riesz spaces (English) |
| Author:
|
Chil, Elmiloud |
| Author:
|
Mokaddem, Mohamed |
| Author:
|
Hassen, Bourokba |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
307-317 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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]. (English) |
| Keyword:
|
orthosymmetric multilinear map |
| Keyword:
|
homogeneous polynomial |
| Keyword:
|
Riesz space |
| MSC:
|
06F25 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 06486995 |
| idMR:
|
MR3390278 |
| DOI:
|
10.14712/1213-7243.2015.132 |
| . |
| Date available:
|
2015-07-09T20:44:23Z |
| Last updated:
|
2017-10-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144346 |
| . |
| Reference:
|
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| Reference:
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