Some notes on orthogonally additive polynomials

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Authors

Schwanke, Christopher Michael

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Taylor and Francis

Abstract

We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using separately two polynomial identities of Kusraeva involving the root mean power and the geometric mean. Furthermore, it is shown that a polynomial on a vector lattice is orthogonally additive whenever it is orthogonally additive on the positive cone. These results improve recent characterizations of bounded orthogonally additive polynomials by G. Buskes and the author.

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Keywords

Vector lattice, Orthogonally additive polynomial, Geometric mean, Root mean power

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Citation

C. Schwanke (2022): Some notes on orthogonally additive polynomials, Quaestiones Mathematicae, 45:10, 1559-1565, DOI: 10.2989/16073606.2021.1953631.