Characterizing Bounded Orthogonally Additive Polynomials on Vector Lattices

2018/03/20 by Gerard Buskes, Buskes, Gerard, Christopher Schwanke +1
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Functional Analysis (math.FA) #Rings, Modules, and Algebras #math.FA

paper · pdf · doi:10.48550/arxiv.1803.07361

arxiv created 2018/03/20 · openalex publication_date 2018/03/20 · arxiv updated 2018/03/21 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

We derive formulas for characterizing bounded orthogonally additive polynomials in two ways. Firstly, we prove that certain formulas for orthogonally additive polynomials derived in \citeKusa actually characterize them. Secondly, by employing complexifications of the unique symmetric multilinear maps associated with orthogonally additive maps we derive new characterizing formulas.

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• Homogeneous Polynomials: Harmonic Means and Completely Partitioned Weighted Geometric Means
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