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Continuous orthosymmetric multilinear maps and homogeneous polynomials on Riesz spaces

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Abstract

We show that any continuous orthosymmetric multilinear map from an Archimedean Riesz space into a Hausdorff topological vector space is symmetric. Then, we establish a linear representation for continuous orthogonally additive homogeneous polynomials. This representation will be used to introduce and describe a new class of homogeneous polynomials, namely that of polyorthomorphisms. In particular, we prove that, for a Riesz space E and a natural number \(n\ge 2\), the space \({{\mathcal{P}}}_{orth}(^nE)\) of all polyorthomorphisms of degree n is a Riesz space.

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Acknowledgements

The authors wish to express their thanks to the referee for stimulating comments and suggestions on the first version of this paper.

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Authors and Affiliations

  1. Institut préparatoire aux études d’ingénieurs de Tunis, 2 Rue Jawaher lel Nahrou Montfleury, 1008, Tunis, Tunisia

    Elmiloud Chil

  2. L.A.T.A.O, Faculty of Sciences of Tunis, Tunis-El Manar University, Tunis, Tunisia

    Abderraouf Dorai

  3. Abderraouf Dorai Institut préparatoire aux études d’ingénieurs El Manar, BP 244 El Manar, 2092, Tunis, Tunisia

    Abderraouf Dorai

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  1. Elmiloud Chil
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  2. Abderraouf Dorai
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Correspondence to Elmiloud Chil.

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Chil, E., Dorai, A. Continuous orthosymmetric multilinear maps and homogeneous polynomials on Riesz spaces. J Anal 28, 1127–1141 (2020). https://doi.org/10.1007/s41478-020-00240-2

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  • DOI: https://doi.org/10.1007/s41478-020-00240-2

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