Some notes on orthogonally additive polynomials
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Date
Authors
Schwanke, Christopher Michael
Journal Title
Journal ISSN
Volume Title
Publisher
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.
Description
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.