Abstract
The aim of this article is to prove a representation theorem for orthogonally additive polynomials in the spirit of the recent theorem on representation of orthogonally additive polynomials on Banach lattices but for the setting of Riesz spaces. To this purpose the notion of p-orthosymmetric multilinear form is introduced and it is shown to be equivalent to the orthogonally additive property of the corresponding polynomial. Then the space of positive orthogonally additive polynomials on an Archimedean Riesz space taking values on an uniformly complete Archimedean Riesz space is shown to be isomorphic to the space of positive linear forms on the n-power in the sense of Boulabiar and Buskes of the original Riesz space.
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The first author was supported in part by Project MTM 2007-62478. The second author was partially supported by the “Programa de formación del profesorado universitario del MEC”. The second and third author were supported in part by Project MTM 2006-03531.
The authors wish to thank the suggestions and observations of the referee that have helped greatly to shape the final form of this article.
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Ibort, A., Linares, P. & Llavona, J.G. A representation theorem for orthogonally additive polynomials on Riesz spaces. Rev Mat Complut 25, 21–30 (2012). https://doi.org/10.1007/s13163-010-0053-4
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DOI: https://doi.org/10.1007/s13163-010-0053-4