Schwanke, Christopher Michael2022-03-242022C. Schwanke (2022): Some notes on orthogonally additive polynomials, Quaestiones Mathematicae, 45:10, 1559-1565, DOI: 10.2989/16073606.2021.1953631.1607-3606 (print)1727-933X (online)10.2989/16073606.2021.1953631http://hdl.handle.net/2263/84582We 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.en© 2021 NISC (Pty) Ltd. This is an electronic version of an article published in Quaestiones Mathematicae, vol. 45, no. 10, pp. 1559-1565, 2022. doi : 10.2989/16073606.2021.1953631. Quaestiones Mathematicae is available online at: https://www.tandfonline.com/loi/tqma20.Vector latticeOrthogonally additive polynomialGeometric meanRoot mean powerPostprint Article